I agree with your outfitter. I don't see that there is a whole lot of difference in any of them, with the exception of if you are maybe thinking of a velvet buck, the later you go the harder it will be for them to still be wearing velvet. On the other hand the later you go the cooler it will be for any hanging meat that you may have. It can still be plenty warm even in the mountains that time of year. I have seen where we got 6" of snow though too, although it don't stay on the ground long, so it's all a crap shoot.
I'd go when ever it's more convenient for you and whatever your desires are. Best of luck to you. That's a good area, so post us a picture of your monster buck when you get back.