A lot of good suggestions. I don't typically post but the earlier comments about excursion in the snow got my attention.
I wanted to offer a Couple quick thoughts - 1st to dispel the notion that excursions are bad performers in the snow. Quite the contrary and I've got plenty of experience to know. At about 8000 pounds and fairly heavy in the rear (unlike a pickup) with appropriate tires and perhaps a limited slip in the rear you should have a solid snow capable rig. Weight is fairly balanced over each axle which is an asset. Not suggesting you go break trails over the sierras in multi foot deep snow, but that's not what you described wanting. I'm also not suggesting excursions are the equivalent of snowmobiles - they are not. But they're definitely not inadequate snow vehicles.
I've got an 05 6.0 ex and it is great in the snow. I find the earlier post by chris to be odd at best about excursions being noted as poor snow performers for what you are describing.
This is my 2nd Ex, traded my 03 with about 60k for the 05 once I learned Ford was going to stop making them. The 05 has 200k+ and going strong. Between the two I've got a lot of miles in snow, both on and off roads between commuting, runs up to Ski resorts, and countless deer and elk hunting trips all over Oregon, Washington, Idaho, Montana and Canada with the two excursions. Not to mention countless taxi trips for friends, family, and employees that can't get around because of snowy roads.
We've got a pretty decent snow dump in Portland right now and a couple so far this year. (Portland is not equipped to deal with snow - any snow. It's comical how paralyzed everyone gets here when the flakes start to fall!).
I typically drive the Ex because it is so good in the snow - and I've got other options -
I have a 2016 Rubicon Unlimited with AEV's full kit and 37" bfg at ko2's, a second set of 37 gy mtr on AEV bead locks. Also a Jeep J20 on 39.5 IROKs (best deep snow tire I've ever seen), Dana 60's, Detroit s f&r, nv4500, f/I built AMC 401 and on and on and on... I've had plenty of others, early broncos, cj's, TJ's, JK's, f250's, f350's, j trucks, and even an M715 (still have the m715). Again plenty of miles in the backcountry including snow.
I'd happily choose the excursion when it comes to the snow unless its deep trail breaking snow runs (the 8k weight is not an asset in the multi-foot deep stuff!).
As it's been said, I think you have a tire problem 1st and foremost. A limited slip would help a lot. You'd be surprised what can be done with appropriate driving technique with only those two things.
Currently I'm running 285 75r16 bfg at ko2's and can say with confidence they are great winter traction tires. Both my excursion had limited slip rear (I had the luxury of ordering them that way). They are also a great back country and even road tire. There are other great tires out there - just select ones that fit the balance your looking for. Whatever you have now clearly isn't the right choice.
Good luck on your build!
Thank you for sharing some real-world experience. I haven't had a chance to experience any decent snow in my Ex yet and I was quite surprised at people's opinions that they weren't good in snow (considering the reasons you listed- heavy, decent weight distribution, etc).