RBF is right.
Sounds like a good set-up, but you're pretty crowded and you need a heater. I think of it like sharing a bedroom with a pet, if you have a small room you don't want a huge bird cage and a hamster too. Sort of like a betta in a small tank won't want a bunch of other things in there.
Though cories are awesome, not for a small tank. I'd wait and get a good pack of them for your larger tank.
My rule of thumb, for the betta's happiness, is one shrimp per 2.5 gallons or one snail per 5 gallons. So my ten gallon could have four shrimp, two snails, or two shrimp and a snail.
Happy fishkeeping to you and hope to see you around.