If you have been doing things like north slopes of San Gorgonio and Mt. Baden-Powell, you should be ok here. You are climbing about 1,000' to Trail Crest...that it. The problems you will encounter will be from Trail Crest to the summit. That is the area that requires most skills this time of year.
I most likely would bring my GPS just to be on the safe side, in case of white out. However, it really is not necessary below Trail Camp, this is a super highway, not a trail. There will be trails cut with all the short cuts between the WP and Trail Camp. With the road "open" to WP, I would be surprised if the above conditions did not exist.
My rule has been if the crampons and axe come out the helmet goes on. This puts me in the minority.