yes it's possible.
It's best if they are mud specific.
Generally, most tires can only go up to around 1" of powder or compacted and about 2" of sticky or slush.
The only advantage studded tires have are the studs that can bite into ice. Regular knobbies can't do that. Studded tires are very close in design to mud specific knobby tires.
The other types are not ideal, but not undoable.