When it gets really cold -30 ish my shower won't shower water. It usually starts working no problem once it warms up a bit. This time the washing machine is saying low water pressure and refuses to to wash anything. What could be possible causes?

Shower is on ground floor, towards the middle of the house, washing machine below shower in basement. ALL other taps, toilets and showers work. Basement is heated, garage is heated, no pipes run outside or in attic space. We are on well water with one of those dome water pressure things. Bit of a puzzle.

Check the well pump and exposed pipes. If the pump get very cold, which it will if not insulated, will take a while before if is able to build up sufficient pressure. Minus 30c (still air) will chill way down in well shaft. Cold air falls rapidly and could freeze even a deep well. Be sure it is well insulated over the top of the well shaft.

Would that not affect all taps though, its just the two things thats playing up?

I guess it would depend on the volume of water being drawn.

You didn't mention if you were trying to draw only cold water through the shower at first.
I'm 'assuming' your washing machine draws only cold water and heats it itself.

If so, you probably have some partial freezing in the cold water line where it enters the house. Need to figure out if the washing machine / shower are the first two things to branch out from the main line, and if the other fixtures are farther down, meaning they have time to draw the water sitting in the pipes first.

The water that we manage to get out the shower (about a 1/4 of the hhead) is cold, even when I leave it running on hot, the washing machine i think also has a hot feed. I'll see if OH can figure out the rest of what you have said. Shower is working today it's warmed up a bit