Is there a temperature at which ice is denser than water? Normally ice would float on water because its density is less compared to that of water as a liquid. 
But is it possible that its density will increase due to a very low temperature or is ice in any case lighter than water?
 A: Ice can be denser than water for certain values of $P,T$. Look at these two pictures taken from here:


The darker areas in the second picture denotes areas of greater density. So you can clearly see that when pressure is increased, ice becomes denser than water along the coexistence line.
For example at $T=400$ K ice VII is clearly denser than water along the coexistence line ($P \simeq 2$ GPa).
Quoting from the page:

As pressure increases, the ice phases become denser. They achieve this by initially bending bonds, forming tighter ring or helical networks, and finally including greater amounts of network inter-penetration. This is particularly evident when comparing ice-five with the metastable ices (ice-four and ice-twelve) that may exist in its phase space.

At atmospheric pressure, $P_{atm} \simeq 100$ kPa $=10^5$ Pa, ordinary ice is always less dense than water.
Upadate: how to read the pictures
When I posted this answer, I may have taken for granted that everybody was able to read this kind of phase diagram, but since it looks like I was wrong, I will try to explain them better.
The first diagram shows the various phases of water as a function of the two parameters $P,T$. The first thing that must be noticed is that the pressure axis is logarithmic while the temperature axis is linear. This means that the plot is "compressed" in the vertical direction (you can see that the $T$ axis goes from $1$ to $800$ (almost 3 orders of magnitude) while the $P$ axis goes from $0.1$ to $10^{12}$ (13 orders of magnitude!)).
The black lines are coexistence lines. This means that along those lines two phases can coexist. If we want to compare water and ice, I think that the only meaningful way to do so is to compare them along the coexistence line, because only there it will be possible to have both of them. For example, you can see that ice VIII can never coexist with liquid water.
Our world is located at $P= 1$bar$\simeq 10^5$ Pa (red line):

You can in fact see that, at the red line, the solid-liquid transition is at $273$ K ($0$°C) and the liquid-vapor is at $373$ K ($100$°C) - as expected.
But things get different at different pressures. For example, at $10^6$ Pa ($10\times$atm.pressure), the liquid-vapor transition is at $450$K, and at $10^2$ Pa ($1/1000$ of atm.pressure) ice sublimates directly into vapor (there is no liquid state!).
Now, the density. You have to look at the second plot to see the density.

For example, let's take the $400$ K-$2\cdot10^9$Pa point (yellow arrow in the first plot). To see the density, look at the corresponding point in the second plot. You can see that the area corresponding to ice (ice VII) is darker than the area corresponding to water, so you can tell that ice is denser than water there, and so on.
If you take P=$10^5$ Pa (atm.pressure), you can see that ice is always less dense than water (lighter shading) there.
