If that is what they told you, that would be a first. I have never heard of water getting into a strut...and don't think it can really happen. Now if they meant that the strut had been blown and was rusting to some degree, that could make sense...but once again unlikely. Feeling stiffer when cold (I'm also in Chicago...) is more likely may other things other than struts. Like tires, seats harder when cold, you being tense...

If water inside the strut froze, it would be hydrolocked and you would have no give in the suspension at all and it wouldn't soften up...you wouldn't want to drive even 100ft with hydrolocked struts.