At well over 11,000' Slumgullion Pass is a high pass. And the north side is said to have up 9% grade ("the steepest grade of any continuously paved road in Colorado"). And numerous sharp turns and switchbacks.
The south side is not nearly as steep and twisting and will not present too much challenge to tow up it. They were repaving the road up the south side last summer so it should be in good shape.
Have driven it several times, but not towed it. But I would rather tow from south to north than vice versa. Just take your time and watch your speed going down and you should be ok. Let the truck do the work, especially if you have exhaust brake. Above all, take care to not overheat the brakes.
From TX you can take I-25 thru Raton to Walsenburg and west on US 160. Two more passes that way, Raton Pass (not bad at all) and La Veta Pass west of Walsenburg (a bit of a climb, especially west bound). Or you can go over to Santa Fe and take US 285 north to Alamosa. No passes that way.