I recently brought my car into a mechanic to fix a problem with the
steering, thye ended up replacing my power steering pump. The day I
picked it up it had trouble switching gears and the check engine light
came on. The next day it wouldn't go above 20 mph or reverse. The
check engine light did go off before I brought it back to them
however, so I wasn't able to identify the trouble code.

I brought it back to them and they told me the transmission went. Is
it normal for a transmission to go that quickly without any warning
signs prior? Should the mechanic have noticed something when
diagnosising my car's problem when I originally brought it to them?

It does have roughly 180,000 miles but it has been very well
maintained and most of the parts are new. I know its a lot of miles
for a car, but the day I picked it up the transmission starts to have
problems? I think its a little strange. If you also think its strange
or somethings not right, do you have any tips on what I should ask
them. I don't know too much about cars and they are a mechanic, I feel
like they would just deny that they did anything wrong.

Also note:  it was driven in a snow storm and thats when the power
steering pump had a problem, but the transmission was fine for about a
week and then the car was brought in, it wasnt until i picked the car
up that the transmission started having problems