i slide into some dudes yard sideways in winter 08/09, no damage to the truck. i drove home right away because a tire was leaking air. got up the next morning and i had flat tires.. i was wtf...i was rolling on a set of brand new 31x10.5x15 BFG A/T's.. i will never run those tires again.. but apparently snow got jammed between the rim and the bead of the tire.. we heated up the rim and melt the snow/ice and it aired back up fine..
when i was home from alberta in the middle of winter one day a few years ago i was driving my old 87 dodge dakota 3.9L v6 2wd and i needed gas, there is a little store out in the middle of nowhere in Roger's Pass. i went to pull in there and slid into the snow bank haha... only pushed the drivers side front bumper in a little bit.. nothing major..
yup stuff happens.your tires should air up just fine, make sure the bead is clean..