Neon Tetras are tropical fish and thrive in warmer waters, 22-26C (72-79F). Therefore yes, you will need a heater.

Also keep in mind the rule of thumb for the amount of fish for your tank is 1inch of adult fish per gallon! Since an adult Neon Tetra can grow to be about 1.5 inches, then for a ten gallon tank you should not get any more than six - seven fish.