Well, we had a blast up at Goose lake this past weekend. The snow was indeed blocking the road and it's going to take at least two to three weeks to melt IMHO. Snow was three feet in some places and fairly solid on top for us to walk on it.
Just for the record, you can't camp right next to the shoreline but the large cul-de-sac parking area is very close. You can park there and pitch your tent in the trees. There are two pics of the parking area below and you can see a gate where the FS is able to drive vehicles to the shore. Since I have a RTT, I'd just setup my camp in the parking lot. There is a pit toilet there which is nice. Traffic wasn't much to speak of, occasionally had to stop and backup or make room for the tour guides but that's about it. We arrived on Friday and setup camp about 1.5 miles below the lake. Next day, we parked below the snow covered road and walked up the half mile to the lake.
Ideally, I'd leave ABQ first thing Friday morning and get up to the lake. If you get there late PM like we did on a Friday, more traffic will be coming down the narrow one way road which could get annoying. If you camp at the top or near the lake, be prepared to see people coming up for the day but I bet things will quiet down nicely by the evening time. The trail starts from Red River so depending on where you camp on the trail, you could go back and forth to town. Another option is to camp elsewhere near RR and shoot up to Goose lake for few hours and deal with the traffic both ways.
This trail is covered with used TPs where people have camped or just pulled over for a potty break. Otherwise, the trail was fairly devoid of trash as far as I saw. The creek crossing was fairly deep at the very beginning of the trail, depending on where you cross it. As you're approaching the creek, stay to the right for a shallower crossing. I went to the left, both directions and my 35" tire got swallowed for a short while. My daughter made a video of my crossing but it seemed to have been swallowed by the ether after I uploaded it to FB, weird. Ron's GX470 is on 32" and 2" lift and he had water over the hood because he followed me inbound. On our way out, he stayed to the right and the water hit his headlights. In any case, don't dilly dally during the crossing and don't go too fast. Just a nice bow wave is all you need to keep water from coming in. My daughter, Isabelle, was filming by sitting on the window and her tooshy got splashed she told me!
If you have an offroad trailer, you should be fine, assuming the contents didn't get too wet during the water crossing. The trail is rocky so a high clearance 4x4 is required IMHO. A F150 from NM was following us and when we pulled over due to deep snow, he wanted to have a go at it. Dad and two sons had to try it, even though a Landcruiser with 35s and a winch had pulled over and parked. He made it even less distance and to be pulled out. His poor plastic skid plate thing was dragging. I'm guessing it eventually fell off and he must've picked it up on his way out.
We soaked at the Mamby hot spring, just outside of Taos on the way home.
Let me know if there are questions.