Your friend is correct in stating that heat capacity is the something to watch for here. As the liquid comes in contact with you, it will begin absorbing heat until it reaches the same temperature as your body. As water's heat capacity is higher, assuming both liquids were at the same starting temperature, water would absorb more heat from your body than alcohol would. This is nothing close to a final answer, however...
You mention the "burning point" of these substances. I believe you meant boiling point. Although you have the right intuition in believing evaporation is important, the boiling point itself isn't. In fact, when water or alcohol splashed on your body evaporates, it never gets to its boiling point (that would mean either our bodies or the atmosphere would be at around 80 or 100 degrees celsius, which I hope never happens). This means that liquids can evaporate without reaching their boiling points. That is what vapor pressure is all about. Vapor pressure can be defined as the tendency of particles to "escape" from the liquid (a higher vapor pressure means a liquid has a higher tendency to evaporate). And as evaporation requires energy, the liquid will need to absorb it from your body for it to happen.
It also has to do with to how your body perceives this "cold". In itself, cold does not really exist. It is only a word we use to describe something as having less thermal energy than some abstract point of reference. In our case, then, "feeling cold" is simply how we describe the feeling of heat leaving our body. The more heat is leaving your body at a given moment, the more "cold" you will feel.
Assuming you are covered in an equal amount of water in situation 2 and of ethanol in situation 3 and assuming you just stand there while waiting to dry in the exact same atmospherical conditions for both situations, your body would actually lose more heat to the water than it would to ethanol. That doesn't mean water would feel colder, however. You need to look at the speed at which that heat is lost.
Normally, since water's thermal conductivity is higher than that of ethanol, it is safe to assume that the rate at which it absorbs energy to raise it's temperature would also be higher (about 4 times faster, in fact). However, alcohol is very volatile, it will evaporate a lot faster than water, absorbing more energy for that purpose. Also, while vapor pressure is a good indicator of evaporation speed, it is normally used in closed systems. While we can still say that alcohol has a higher tendency to evaporate, we can't say for sure how much faster it will happen.
You also need to look at the amount of each gas (water and alcohol) present in the atmosphere. If the atmosphere is saturated for a specific gas, it will be harder for the same liquid to evaporate. In the case of ethanol, one can safely assume that there are only traces of it in the atmosphere. Water, on the other hand, is a very different case, as there is normally a good amount of it in the atmosphere. That amount of water in the atmosphere can be given by relative humidity. We also know that evaporation speed is inversely proportional to relative humidity. This means that, while there is nothing preventing ethanol from evaporating, an atmosphere saturated in water vapor (high relative humidity) could prevent water from evaporating at a normal rate.
Considering all this, it is very hard to give a definite answer to your question. Normally, water would absorb heat faster than alcohol and be able to absorb more of it to boot. However, the fast rate at which alcohol will evaporate means that it will need to absorb more energy, which can tip the scales. In the right atmospheric conditions (high relative humidity), it is possible that this could mean alcohol feels "colder" on your skin.
Now, if you would allow me, I would like to get you into thinking more on the matter.
Your hypothesis was, I guess, based on personal experience. However, I doubt you recorded relative humidity at the time of the "splashing", nor measured the amount of liquid involved. Also, while your body is indeed able to send a stronger signal to your brain when more heat is lost, it is not exactly the best tool to mesure heat transfer. In fact, your body can be fooled into thinking very weird things when it comes to heat.
I suggest, if you are willing, to do the following experiment before continuing to read this answer:
Fill 3 bowls with water
- The left one with cold water (cold tap water and ice cubes works fine)
- The middle one with room temperature water
- The right one with hot water (from tap, just don't burn yourself!)
Place your left hand in the cold bowl and your right hand in the hot
bowl and keep your hands submerged for about a minute.
Then, simultaneously place both hands in the room temperature water.
How do you feel? Does the water feel as "hot" or "cold" for each
hands? It should, no? After all, they're in the same bowl filled with
the same water at the same temperature...
What I mean by this experience is that, although we can describe the science behind the feeling of cold while being splashed with water or alcohol, your body simply isn't the right tool to make accurate measurements of the situation. As I said, your hypothesis was likely the result of previous experiences. However, if even the temperature of your skin can influence how you perceive heat, could it not be possible that those experiences could not, in fact, be compared with one another?
In a lab, we could run a simulation where water and alcohol at room temperature are placed on two identical sheets of metal (or better yet, a substance with heat related properties similar to skin) initially at the same temperature (around 37 degrees celsius sounds like a good idea) and let them stand for 5 seconds, a long enough time for a measurable amount of heat to transfer, yet short enough that it's not too unlike being splashed by water. Aterwards, we could calculate how much heat as been transfered to each liquid by measuring the drop in temperature from their respective sheet of metal. Divide the total heat transfered by 5 seconds and you get the rate at which each liquid absorbs heat, with a higher rate of absorption meaning a theoretical "colder" feel from your body.
And even then, it would still be impossible to guarantee that one of the liquids would definitely feel colder than the other. Only that it's more likely to do so, since it's impossible to splash you at the exact same place at the exact same time with both liquids so you can really say that no other factors could've influenced your perceptions.