Steering wheel Problem

I have a 1997 Mazda 626 with 39,000 miles on it. Recently my steering wheel has been difficult to turn and seems sluggish. I checked the steering wheel fluid and it is full. We have been having very cold weather. Could this be the problem? Also my brake light does not turn off when the brake is not engaged. I will appreciate your help. Thank you.

The power steering pump may be faulty or you may have a worn out rack.

Check that the brake pedal arm is disengaging from the brake light switch. It (the switch) likely just needs an adjustment.

Have you checked the tire pressure? One low tire can do it. If you do find a seriously low tire then the tire should be examined carefully because the sidewall could be damaged. This can lead to a blowout.
Agreed with the brake light switch diagnosis.

you might need to bleed the power steering fluid that meens that you need to drain all of the fluid (not just the one in the tank but all of the fluid) and put new fluid in it.