Gary,

In Utah whether or not you are engaged in a hunting activity has no effect on the privilege granted by the Concealed Firearms Permit. Permit holders are specifically exempted from the loaded firearms in a vehicle sections of the code. This used to be outlined in the Big Game Proclamation, which no longer exists. It is now the "Big Game Application Guidebook" and far less comprehensive.

Aside from this there is no restriction as to the number of firearms you may have in your possession, so long as they are legal for the game currently being pursued and the specific season.