Timber shed door swelling in winter

The door of my timber shed swells so badly in winter that it jams solid and can't be opened. Last summer I planed a few mm off the edge next to the lock which was fine at the time but since about November it has been jammed solid again. I'm reluctant to take any more wood off in case it just creates large gaps so am looking at better sealing of the wood. The shed has had a coat of timber preservative (Cuprinol Ducksback if I recall) including the edges and top/bottom of the door but after doing some Googling it seems that these preservatives don't seal the wood and it is the lack of sealing that causes the swelling. Apparently an oil based primer and top coat of paint is required to seal the wood to prevent it swelling. Has anyone else had my problem and gone down the paint route?

 

I dont think it matters much what you use.

Timber swells when it gets damp and shrinks when it dries out.

The trick is allowing for that during construction.
If its a boarded door it should have room between the tongue and groove joints to allow for swelling.

Not sure how they make sheds these days, but traditional methods allowed for the movement.

 

Same problem here,so I cut the door down and added an extra door stop strip to compensate when it shrank back in the warmer weather.