I'm just going to make a few final comments and then withdraw from this thread.
Oxygen ingress is not binary, i.e. it's not "have it" or "don't have it." There's a huge range of possible amounts of ingress and thus oxidative impacts.
I don't have nearly enough information to compute how much O2 is entering during your cold crash. But I can say very confidently that it's more than during an equivalent amount of "stationary" time after active fermentation. How much it will affect your beer flavor stability also requires more information than we have. You might not notice anything special. Or you might. And others might taste it differently, depending on their own flavor thresholds for various oxidized compounds.
My main message here would be that looking at oxygen/oxidation as more or less binary is not an accurate view. If you're curious to learn more about how gases behave, the wikipedia pages are actually pretty good for a start. I'd recommend:
https://en.wikipedia.org/wiki/Gas_lawshttps://en.wikipedia.org/wiki/Fick's_laws_of_diffusionhttps://en.wikipedia.org/wiki/Henry's_law
A basic understanding of the above is enough to work logically through most scenarios encountered in brewing. And if not, there's always
@Vale71 and
@doug293cz.