Okay there is probably your problem. He might be getting some ammonia poisoning, usually snails aren't good for smaller tanks because their bio-load is so big that they pollute the water very quickly.
Not having a filter is fine, I'd much rather you have a heater anyway :) And, just be careful it doesn't overheat your water. Start at a lower temperature and work your way up to the place you want to keep it at, having a thermometer will help with that because sometimes what the Heater thinks it's heating at is actually higher than what it is heating at, if that makes sense.
If at all possible, and I'm sorry to say this, you might have to either get rid of your snail or upgrade to a bigger tank like a 5.5 or 10 gallon for them to live happily together.
There are small siphons you can get like this one here:http://www.thatpetplace.com/aqueon-siphon-vacuum-mini-5
which are great for smaller tanks and is still cheap :D Because unfortunately stirring it up isn't going to help get all the poo out of there. It's only going to cause you more problems :/