When I start my car, the engine rev  to 2,000 rpm before idling at below 1,000 rpm. I am concerned that revving at this speed when the engine is cold may cause premature wear and tear. What do you think?

It is normal for a car's engine to rev at a higher speed for a couple of seconds during cold starting. The engine speed will then drop to idling range.

When engines are cold, especially in cold countries, the mechanisms are tight. The high compression of the petrol engine yields a very high mechanical resistance for the first few seconds upon starting. 

The engine needs to run at a higher speed to overcome that resistance and keep running.
As long as you are using quality engine oil, this should not harm the engine.