The best resource I have found for any questions on Concealed Carry in Utah is http://www.utahconcealedcarry.com
Currently you CAN carry your gun in National Parks, (not any buildings in the parks), you just have to follow the laws of the State you are in. This law was passed with Obama's Credit Card bill that went through a couple months ago. Also concerning car carry anybody that can legally own a gun can carry loaded (in the chamber) with or without a permit in Utah. The only thing you have to watch is going through a School Zone if you don't have a permit (this is violating the Federal Gun Free Zone Act).