I have thought about it. both for the former 2-children trailer and the current Nomad trailer, but I haven't done anything yet. It will likely procrastinate for a few years. Adam K., though, has done it and he shows how here (towards the end)

Basically, rain (light or heavy) tends to splash behind the trailer, and therefore not on me. If I also have my rear panniers, they often receive a few droplets, nothing more. I suspect it would be a problem if I were to ride in the rain in fancy clothes, but with my typical clothing – city compatible, usually in neutral colours – these drops would not be noticed. And if I have the rear panniers, nothing flies back on me. Snow and slush are different: because they are heavier, they stick more and the trailer wheels throw some definite chunks either on me or my rear panniers.

The main "problem" with rain is that it makes the trailer dirty. And riding in winter makes it filthy.

I do. Typical Winter conditions (ice, hard-packed snow, etc.) are not a problem. If you climb a steep hill, you might notice that you don't have enough weight on your own rear wheel for traction on ice. That's when you learn to spin smoothly!
Fresh snow is a bit more problematic in that you dig your trail. If you find that digging a single trail in 10-15 cm of wet snow is a problem, think of the workout you'll get when you dig three such trails!

Typically, when the kids were young, I used the trailer regardless of the weather. Now that I use the trailer for cargo, I try to avoid using it when it's messy. Considering our weather patters, that typically doesn't require too much planning.


And finally, one aspect to consider. If you use a child trailer, the plastic "window" becomes brittle at around -15 C. On my former trailer, I had a lot of tape on that window.