A. Many Orthodox men DO wear wedding rings. There is nothing wrong and many things right with men wearing a wedding band to show fidelity, love, commitment etc. Although I must add, there’s no double-ring ceremony under the Chuppah in an Orthodox service. That’s not allowed for Halachic reasons stemming from the biblical text on marriage. Usually the bride would give her husband his ring in the Yichud Room (the private room they retreat to after the Chuppah).
But you are right that most ultra-Orthodox (Chassidic, Litvish etc) men do not wear wedding rings. That’s because those men don’t wear jewelry altogether. You won’t find those same men wearing Chai necklaces or gold bracelets either.
Wait, you ask, so how to tell the married ones apart from the singles? How to know who is available? First of all, these are often much closer-knit communities where people know people. Also, on Shabbat (depending on specific community) there are identifying clothing that mark a married ultra-Orthodox man from an unmarried one. Most ultra-Orthodox (and I hate that label) men don’t wear a Tallit before marriage, and many begin to wear a longer black coat after marriage. So there are ways to tell.