Can low temperature plasma exist? Plasma is ionized gas which as far as I know only occurs at high temperatures. When plasma cools down it tends to recombine with the electrons present and turn back into gas. But what if the disassociated electrons in the plasma were removed and the plasma were allowed to cool down in a vacuum, while being held in place by a strong magnetic field. Would this substance still be plasma? Is this possible?  
 A: By definition, a plasma is neutral.

Plasma is loosely described as an electrically neutral medium of positive and negative particles (i.e. the overall charge of a plasma is roughly zero).

There is such a thing as a non-neutral plasma. You can construct these by storing charged particles in a Penning trap. These don't display the kinds of properties that you expect from neutral plasmas. For example in neutral plasmas there is a "screening" effect where, because the charge carriers are fairly mobile, any concentration of charge is immediately surrounding by opposite charge, limiting the radius over which its influence is felt.
Note that the electric force is incredibly strong. Depending on how you measure it it's between around $10^{39}$ and $10^{42}$ times as gravity. So even a tiny amount of completely charged plasma would be very hard to contain.
A: There is also plasma in outer space, mainly Hydrogen and Helium nuclei, with a very large range of temperatures.  Much of it is very hot, but much is also cold.
See for example http://en.wikipedia.org/wiki/Interstellar_medium
Meanwhile, on Earth, experiments have been done on trapped particles, some of which are ionized.  It would be a bit misleading to call this a plasma, as they are being held apart (as you said in your comment) by an e-m field, but they also can sometimes strongly interact with each other.
A: If the density is extremely small, the recombination rate of free electrons with ionized atoms (or just protons) can exactly balance the thermal ionization rate even at reasonably low temperatures. It depends on what one calls "cold", and also what fraction of neutral atoms (a few percent, or only one part in a million ?) one accepts and still calls it a plasma.
But yes, in principle, a plasma can be cold if it is extremely dilute.
Choose a temperature, a given fraction of atomic hydrogen, and there will always be a density low enough that the equilibrium of the plasma will be reached at your chosen temperature and you chosen fraction of atomic hydrogen. With one electron and one proton per cubic parsec, I guess you can get only 0,01% atomic hydrogen for pretty low temperatures !
