But the mud is fun to scrape off.......
You should be fine, just realize that if you brake hard on a curve, especially a downhill curve, the trailer will want to push the rear end out. This is easily corrected by using the throttle, but if you could use the throttle, you wouldn't have been braking so hard......
So anyway, take it easy and slow down for the corners.
Reviving an old, old thread because I have a long story about why you do NOT want to tow a pop-up on slick roads.
This past fall I towed my 2800 lb pop-up with electric brakes to Yellow Stone for a two week vacation. All went well on the way out. We had a blast (this was our third trip there, first with the pop-up).
The last night we were there, the weather turned, and they were predicting snow for the next couple of days starting around noon the next day. So we planned to leave around 4:00 AM local time (We stay on EST when traveling to stay ahead of the crowds.) so we could get across the mountains long before it hit.
We got up at 3:00AM and just as we finished packing it started very lightly snowing!

I have a 4WD Nissan Xterra so we decided to go ahead and start up the mountain to beat the snow before it started sticking to the roads. The temps had been in the 60's for the last couple of days so I didn't think the snow had any chance of sticking before we could get across....
Everything was going fine until the wife noticed that the temps had plummetted into the high 20's as we climbed above 7000 feet. The roads of course were wet from melting snow but less than a mile later I felt the rear tires spin a bit as I accelerated. ( I was still in 2WD at the time) I pulled off the road and put the truck in 4WD HI, we conferred and decided to go on since we were only about 6 miles from the peak and it was 20 miles back to camp.
By the time we hit the peak the roads were slick and it was snowing hard. We stopped at the top to talk to some construction guys that were there and asked for some 'local' advice. They all said that the storm brewing was going to dump 4-6" and since it was down hill regardless of whether I went forward or back they said go forward but go to 4WD LO and take it easy. I went to low and we started down. When the first curve came up I decided to slow even further then the 10mph I was doing by putting the auto tranny into second.

Big mistake! I have towed that camper and my boat for tens of thousands of miles with no issues on wet slick roads, but had never had either of them on a snow/ice slick road.
The INSTANT I dropped the tranny into second the wheels locked up! I know all you experienced mountain folks are shaking your heads about now, but what can I say, I had no experience with these particular towing conditions and was between a rock and a place. What I should have done was go back to 2WD and my ABS would have worked to help me steer out of the mess I was about to be in. (No ABS in 4WD)
Anyway ass sight being 20/20....
The curve we were approaching was cambered into the mountain, but there was no guard rail. It dropped off a good 200 yards straight down. My wife immediately started screaming as the trailer pushed the rear of the truck around into a jack knife. Both vehicles then picked up speed and we were sliding toward the drop off...
You know how time slows down whenever your life is in danger? Everything was just slow motion. I knew that if God or somebody did not intervene we were going to die, it was that simple... I did the only thing i could think of doing besides joining my wife screaming, I floored the gas pedal and turned the truck into the mountain. VERY slowly the direction we were sliding started changing toward the ditch against the mountain. I was praying that some vehicle did not pop around the curve and I took us all over the mountain. Then I did the one thing I later realized saved our butts. I let off the brakes on the truck completely and reached down and manually applied the trailer brakes on full. The trailer immediately skidded and pulled the truck around so we were facing uphill sliding backwards! The trailer slide off the road in to the ditch where the brake actually could work in the gravel and we came to a stop. Engine still running, wife still screaming but holy crap we were in one piece! I hit the gas and pulled us completely out of the lane and idled up to a flat spot. I shut the truck off, got out and went around to the passenger side to get the hysterical wife calmed down. After that I surveyed the damage. The front plastic part of the camper was destroyed from smacking the side of the truck in the cold temps, there was a nice big dent the the rear quarter of the truck, the dual Trojan 6V batteries were ruptured and acid was dripping all over the place but that was it. So there you have it. See pics for the damage. We got calmed down, got back in the truck, took it out of 4WD, and continued down the mountain. 3 miles later the snow stopped and the roads went back to just being wet. At the bottom we used duct tape to hold all the flapping pieces of plastic and continued on to KY.
Hope you enjoyed the long story and learned something from it.