Was there a standard size for the white star on US cold war tanks or were there several sizes? What size was it? Thanks!

I don't really recall seeing pictures of white stars past the mid-1960's. Certainly by the MERDC / MASSTER era the stars were small black ones on vehicles.

You're probably looking at the FTX of Nuclear Winter and Big Lift for the last major usage of white stars.

From Technical Bulletin TB 43-0147, December 1975, paragraph 2-2(g):

National Symbol: The National Symbol will be the largest size
practical for use in the available space, but will not
exceed 36 inches measured between opposite points.
The star will not be applied in sizes less than 6 inches
between opposite points.

This version of the TB would have been applied to most of the equipment in Army service, both in-service and stored in POMCUS sites for exercises. In the later 70s, the use of the MASSTER and MERDC schemes eliminated the use of the white stars on combat vehicles.

Do they all have to be the same size on each tank or can the size vary???

Most often they were big stickers, so generally uniform. For the most part, it was the same as the WWII version. So, most of these are gonna be old semi-gloss OD .. lusterkess Forest Green would be about the transition to black markings.

That TB referenced above can be found inline and has some examples.

As mentioned above, the white star went away and replaced by a 5 inch black star when camo came into use.

Here’s my Cold War M60 w white stars: