Civic Shifter problem

I have a 1990 Civic LX with Auto trans. When it is real cold in the winter, the car is put in PARK (usually in the morning), the 'P' light on the dash does not illuminate and we cannot remove the key from the ignition. After it sits for awhile running, the light comes on and the key can be removed (I presume it warms up). Usually in the winter afternoon it will not do it (once again warmer I guess) and it never happens in the summer time. Any ideas or fixes for this problem will be appreciated. Trying to get it fixed before the upcoming winter. Thanx

Auto shift linkage gets frozen? There is no telling unless you crawl up under the car and look at it. Anything can happen in the winter, especially to a 15 year old car...