Hi, I think I know what has happened to you.
You asked if cold weather will affect the steering pedal, and the answer is yes.
What has most likely happened, is that your control pedal has gotten wet, then froze somehow, might have been snow, could have been ice, it could have even been just plain old fashioned condensation.

When it gets cold the moisture will condense, and attach to almost any surface, and has likely caused a slight corrosion problem.
I would take the bottom off of the pedal, and try to clean the contact points inside the pedal, as this is the most likely cause. Now if there is a separate switch for directions, I would look at cleaning the contacts inside it as well.

Also, wires can corrode with moisture, so look to make sure that where the wires hook up there is a good clean mating surface, that way the wire gets a good connection.

Now, what might have happened as well, is that when you stowed the boat, somehow the wires the the steering controls got damaged somehow.
You may have to use a circuit tester and check each wire for continuity, that way you know if there are broken wires inside the wire casing.

Ihope this provides some guidance for you today, and happy boating !