I do know the 182RG is not good for grass or rough surfaces since the wheels are quite small in diameter compared to the fixed gear variant. 172RG has the same problem.
The Turbo O-540 in the 182RG is carbureted. I remember my mechanic showing me a TR182 in his shop saying it was a bugger to get set up properly.
For flights through the mountains, I would think the TR182 would be best for your mission, and also for the short fields if they are paved. There will obviously be an insurance premium with the RG to consider. Everyone I've talked to with a turbo says the climb is spectacular with lots of power all the way up to the critical altitude, which would make me think it's best for mountain flying. If I was looking for the simplest plane of the two that still did a good job, I'd say the fixed gear 182 with the Texas Skyways.