How come 'ou' was reduced to 'o' in the US?

The pronunciation is the same, so you can't really say that some "say" this while others "say" that. It's strictly a spelling difference.

These are among the reforms introduced by Noah Webster in his dictionary, with a view towards (a) simplifying the spelling, and (b) creating a distinct American English. (The root forms of many of these words indeed lack the u - for example, Latin color, Italian favorito - so that may have been another motivation of his as well.) So these forms prevailed in the United States, while in the rest of the English-speaking world they kept the original spellings.

Not sure how to post a comment, but this is an interesting use of Google's Ngram Viewer. We can see that between 1840 and 1850 color overtook colour (using their American English dataset).

The reduction of 'our' to 'or' happens when the ending is unstressed (my accents on the stress):

cólour, flávour, hónour, néighbour, rúmour, lábour, húmour

but not when it is stressed

contóur, velóur, paramóur, troubadóur

This is very well explained (surprise) in Wikipedia

I have heard an alternate explanation - Newspaper reporters would telegraph their stories to the main office for inclusion in the paper. Saving space and reducing the cost of the transmission was important so editors issued a decree to drop 'useless letters' from spelling. Since newspapers were the most distributed mass written product to all levels of American society the spellings they used became the standard.

I have some problems with this - for one I've had a hard time verifying it, for another - I thought telegraph operations were charged by the word - not the letter. From some experience (now 30 years ago - who sends telegraphs now ??) there was a 10 character limit on a word - over 10 characters you got charged for 2 words. Was this the case in the mid 1800's - who knows.

I would image the actual answer is some compound of all of the formal attempts to simplify, common usage and general evolution.