Yep, I managed to accidentally cycle a 2.5 gal unheated, unfiltered snail tank. It kept the cycle for months, then I decided to put in a heater and filter and added a betta. I never lost the cycle.
If anyone wants to try it start with some anacharis and around 5 ramshorn snails, I used gravel as a substrate but sand should work. Feed the snails every 3 or 4 days. Put the tank near a window so that the plants get some light and do 50 to 75% water changes every week or two. After 2 months decide to test the water just to see how bad the tank is doing and discover that the thing cycled all by it's little lonesome self. I suspect the key to the whole thing was the fast growing anacharis, it acted as a filter and helped rid the tank of some of the ammonia and nitrates.
You can have a heater without a filter if you use something like an airstone to keep the water moving. I don't use filters when I set up a 1 to 2.5 gal hospital tank, but I do use an airstone and heater. I've tried it without the airstone and ended up with the water being warm near the heater but cold at father side of the tank, it can be a 3 to 5 degree difference in temp.