I don't have an L series, so not sure if any of this applies to your problem, but I had the same issue on my B3000 with my front mount snowblower. On the B3000, the valve body is controlled through cables connected to the joystick.
I did initially attempt to lubricate the joystick, thinking that it was causing the problem, but it didn't help any.
Upon investigation, I found a spot where the plastic sheath on one of the cables was worn through to the steel inner core. Turns out the cable was rubbing on part of the frame under the tractor. This allowed moisture to get into the inside of the cable. When cold enough, the moisture in the cable would freeze, making joystick movement very difficult, almost to the point of being impossible. I ended up removing the cable from the tractor and brought it inside to thaw out. I dried it out as good as I could with heat and compressed air and put some weatherproofing heat shrink tubing over the area to seal it. I may replace the cable eventually, but for now, it is working fine after the repair.