2003 Corolla skidding problems

I have a 2003 Toyota Corolla. In the last year, my car has been skididng/sliding whenever I hit the brakes, especially when it is wet or icy. I do not have ABS, but it has gotten to the point that it is sliding just about any time I brake, especially if I am driving with any kind of speed. It has been looked over by a mechanic & he changed the rear brake pads, but all brakes have been checked, tires are fine. Any idea what this us> Or has anyone else had this problem?

It sounds like you are in need of a set of four WINTER (not snow) tyres. They will make a big difference.

Is just one wheel locking up and the other 3 don’t? Or, the front brakes hold and the back brakes lock and skid?

You tires may have tread but they may be old, or just crummy tires. How many miles on the car? How many miles on the tires? How old are the tires? I am suspect of the tires are fine comment.

proportioning valve?

According tp the mechanic, all 4 wheels are locking up.
My car has 60,000 miles and the tires were replaced at 40,000.
I am no tire expert, but I had both the mechanic I brought it to today & the Toyota dealer a few weeks ago check the tires and rotate them. I was told by both that the tires were fine.

Tires.
Last summer I dumped 4 summer tires with app. 25k miles of thread left on them, but on any other surface than dry asphalt, my car was all over the road. They were 5 - 6 years old high quality tires (otherwise) and had done around 40k miles and looked fine in all aspects.
Any age related problems will be even more - how do I write this - pronounced? (sorry, i’m just a stupid danish guy), in cold weather and on ice/snow.
I’ll suggest that You buy 4 quality winter tires on rims and get 4 really good summer tires for the rims on Your car.