As a simple overnight carrier, don't forget a saddlebag such as a Carradice Nelson or equivalent. They are really well suited to MTBs, although may need a rear rack to keep the load out of the back wheel.
I have a short notice two day tour planned for this coming Saturday and Sunday. Keep your eyes peeled for more MTB Touring shenanigans. The route is planned as Hull to Hornsea and is a slight variation on a previous ride completed my a friend and I. Approximate mileage is 40 miles on day one and 25 miles on day two. Easy peasy.
Watching with interest. been looking at two wheeled trailers on fleabay as i don't travel light. Thinking Mrs HM drops me off two days ride away and I head home.
or vice versa. Not pulled a trailer since my two were tiny. (19 now) Could pick up a cheap kids one and convert it. Get somewhere, set up, and then pootle about to pub etc if need be.
Did a sub-zero tour early this year in France with my son. The main thing you need is plenty of layers - it's easy to overheat when riding, then chill when you stop. I carried a down jacket on the top of the rear rack - whenever I stopped I put it on (along with a hat). It also makes a handy extra layer over a sleeping bag. I ended up sleeping wearing a fleece base layer inside my sleeping bag.
Typically my winter layers are Helly-Hansen fleece leggings with Ron Hill tracksters on top, Helly base layer shirt, fleece jersey then a pertex windproof. Waterproof jacket and overtrousers are essential as it's easy to get soaked and hard to dry out. Pack them on top!
Most other camping things are the same - a tent with a decent size porch for cooking is a must - it acts as a windshield and rain shelter. I prefer a fast powerful liquid fuel cooker like a Coleman or MSR so hot food and drinks can be prepared pronto. Gaz is OK provided you have a good solution for wind protection, but can be poor when very cold.
Of course the winter is often quieter in hotels so they are cheaper and generally available, which is a big help if you don't fancy camping and want to travel lighter. A Travel Lodge might not be the last word in exotica but can be a cheap overnight stop.