If you have it set to Auto, it may be trying to use the a.c. to dehumidify the air (even in cold temperatures). IOW - the fact that the snowflake symbol is lit may or may not have any relationship to the belt having been removed. Can you manually turn the snowflake off?
Likely the belt was removed because the compressor is locked up, or the system may have a refrigerant leak that the previous owner didn't want to repair and so removed the belt.
I would first determine if the compressor is locked up, and if not, see if it has a charge, i.e., install a belt and see if it cools and go from there. Would be surprising if the belt was removed to find that the system is 100% A-OK, but who knows until you try.
'98 LXi - Later Concorde gages (black w/ chrome rings)/'99 LX - LHS gages (white) - HIR bulbs