Why is my 2002 Chevy Blazer overheating?

I have a 2002 Chevrolet Blazer that I bought over the
summer and never had any problems with it since then.
After the snow storm we had in Indiana last week, it
started overheating (got stuck in some snow and had to
work to get it out, not sure if that or the weather has
anything to do with it), it gets up to 260 degrees or more
within 5-10 minutes of being driven. I tried to blast the
heater but it's only blowing out cold air, the heat has
always worked perfectly prior to this. It doesn't make any
noises and seems to run fine other than this. The coolant
levels are also fine. I've read around a little but just wanted
to see if I could get some advice before taking it
anywhere. Thanks in advance