Assalamualaikum
There's a difference of opinion as to whether snail is Haram or not. Some consider both land and sea snail as impermissible to use. Some say only sea snail is allowed. Some say both of them are allowed if cooked properly.
Here,You meet with two conditions
•If you consider it Haram, then you shouldn't use the cosmetics which make use of it.
•If you consider it halal, then you have two options - )Do research as to how it was slaughtered and which kinda snail it was, sea snail is preferred 2)check If there was some impurity and whether a substance was added which made its impurity go away.
According to islamqa:
The use of soap is permissible though it might have ingredients of Haram animals or Halal animals not slaughtered properly because their nature changes during the process. As far as the shampoo and cosmetics are concerned, if it is found out that it has fat of Haram animals and its nature did not change then its use is not permissible. If the nature of this fat changes after processing then even its use will be correct. But until it is confirmed a Fatwa cannot be given regarding its Hurmat (being Halal or Haram) though if one avoids such doubtful products then it would be an act of piety and scrupulousness.