Really p***es me off when customers say "oh it's only emulsion, it's water based so it'll come out" DUHH
The water is long gone, it's what's left behind that is the problem.
White spirit will work on gloss paint but nowhere near as well or quickly as acetone. It is not the right solvent for emulsion.
As said above, heat will soften it up, but I would give it a good pre-soak first, just with water. If it's on wool and the paint is old, probably not going to be 100% successful before you start to damage the carpet. If it's polyprop it should fall out