Hi Tina-
The closest Tridentine Mass to my home is three hours away, so I’ve only gone once, although I wish I could go every week. At the Mass we attended only about half the women were covered (I was surprised more women weren’t covering!). I wouldn’t think people would be offended if you came to observe but didn’t cover, but I guess it would depend on the parish and whether or not everyone did it. Others who attend a Latin Mass every week, might be more helpful on that note…
…but I wanted to write in to say that you might feel more comfortable if you wore a hat. Then you would be covered, but in a way found in quite a few cultures and religions (my husband always points out to me that the women with Irish heritage where he was from always wore hats instead of chapel veils, even in his mom and grandmother’s generation).
I love winter because it’s a lot more common to wear hats, so it doesn’t stand out as much (then again I attend a parish where I’m the only one who covers!).
People might think that you’re Catholic just because you’re there (people thought that I was Catholic before I converted when I attended Mass with my husband, just because I was in attendance regularly) but that shouldn’t really be a problem. I only heard that later after I’d joined the Church, when someone told me they were surprised to see me at RCIA because they’d thought I was Catholic.
I hope this helps a little! You’ll probably get lots of good answers here.