My dictionary defines すっと with these four meanings:
- 真っすぐ，ほっそりと (straight or slender)
- 素早く (quickly)
- 滞りなく (without delay/obstacle)
- 気分がさっぱりと (refreshed/neat/plain feelings)
So what do all these have in common? All of them vaguely mean smooth. I'd describe すっと as pretty much an onomatopoeia (though I don't think it's officially classified as such). In English you may say zzzzzzip.
すっと伸びた枝 - a branch growing out straight
"The branch grows out like zzzzzzzip." (smooth and straight)
すっと立って老人に席を譲った - He immediately stood up and gave his seat to the elderly
"He stood up like zzzzzzip." (in a flash, smoothly, without delay)
彼はすっと大学に入った - He was admitted to college straight out of high school
"He was admitted like zzzzzzzip." (smoothly, without delay)
よく寝たので頭がすっとした - As I had a good sleep, I feel refreshed.
"My head feels like zzzzzzzip." (fresh, clear)
For your case, I think neither quickly nor gently translate very well:
"The snail extended her horns like zzzzzzzzzip."
In the case of a snail, that probably means both smooth and fast (as far as snails go). The horns just extended like すっと.
I hope this gives you more of a feel of how this is used. When used in speech, accompanied by a hand motion, it's pretty much self-explanatory. :)