It's also possible that the officer in question purchased that hoodie because hoodies are warm and he likes its design, and that he happened to wear said hoodie

It's also possible that the officer in question purchased that hoodie because hoodies are warm and he likes its design, and that he happened to wear said hoodie on election day because it was cold. I don't really think it makes sense to speculate either way. The US military is not a partisan tool nor a domestic political estate, so that message is not overtly supportive of one candidate or the other.