With your size rigs you'll have no problem if you want to stay in the park itself. With our 40' motorhome and Jeep we've stayed at Mammoth, Madison and Bridge Bay campgrounds. We didn't stay at Fishing Bridge with hookups but their RV limit is 40' and your truck will be parked alongside it so there's plenty of room.
Weather? We had very nice weather when we were there. Yes, you'll definitely see snow on the ground but it didn't snow when we were there. It's a beautiful time to go and all the baby animals will be out.
Closely monitor the park's website for road open times and campground openings. Sometimes the dates given will change depending on the weather. At some times, not every entrance to the park will be open.
https://www.nps.gov/yell/planyourvisit/parkroads.htmThe website has lots of good information on campgrounds, things to do, special alerts, etc. Click on all the sections and read them.
Enjoy your trip!