My Poor Little Basil Plant...HELP!?

I received a gorgeous little basil plant for Christmas....and three days into owning him, he is wilted and turning the color of a dying plant. I don't know what I am doing wrong. I don't water him that much (could this be a problem?)...and I tried to keep him in the sun, but we have around 8 inches of snow on the ground here...so I fear that sitting by the window is too cold. I am not sure how else he can get sun though? Is there any way to revive him or should I just try again? And how can I help him so he comes back to life? Thanks!