Does chain tension change how hard/easy it is to pedal? I ride a single speed bike and it seems to be tougher than it should be to pedal. It is comparable to one of the higher gears on a multi-speed bike. I'm getting the feeling that my chain may be too tight.

It has a 44:16 gear ratio.

Would a looser chain make it easier to pedal?

Obviously you don't want the chain too loose or you risk having the chain pop off.
If the tension is too high, the drivetrain will bind. If it is too low, the chain will drop (which is dangerous on a fixie, since it can catch and lock up the rear wheel relatively easily). 

You basically want the highest tension such that the drivetrain doesn't bind. 

See Sheldon Brown on how to set chain tension properly.