First off, your joystick in a cab model is cable connected to the valve block so other than a frozen (rusted) cable it is highly unlikely that the culprit id the joystick itself.
Now, the valve body itself where the cable from the joystick attaches could get moisture inside and freeze. I never had that problem on my 5030 even though I washed it quite often and my new M9, well, I can't speak for that yet, but, I run a roll-off scrap trailer as my day job and I had problems with the controls sticking in cold weather. I drilled a "weep" hole in the actuator body right where the actuator cable screws into the cast boss on the side of the valve body with the hole facing downward. When I disassembled the actuators prior to drilling the holes, both actuators were filled with waterlogged grease which was freezing in the winter. I cleaned out the actuator bodies with a couple spray cans of brake cleaner and then coated the actuator rods and cable attachment points with synthetic grease, drilled a 1/16" hole in the bodies and reassembled the bodies with the hole pointing downward. To this day I can't understand why, that on a $60,000.00 trailer some engineer didn't think of putting drain holes in to let the moisture out.
My symptoms on the trailer were the same as yours....below freezing, sluggish controls. Actually, if I raised the hoist and actuated the winch at the same time, the controls would freeze in whichever position I had them in and I'd have to actually pull them to a neutral position. Very dangerous when dealing with a 60 ton winch and a 50 foot hoist frame.
You have an advantage in that you can actually warm up your hydraulic fluid to a point where it will cause the frozen water to become liquid and allow control movement. With a roll-off, you never get the fluid warm and the valve body is right out in the elements on the side of the trailer.