Is it possible for a man to have HPV and not have any visible symptoms from it?

Yes. Yes, this is very common. Some HPV strains cause genital warts, which of course may be seen by the patient. However many strains of HPV do not cause any signs or symptoms. In women, we can detect HPV by doing pap tests. However, for men, there are no similar tests.
Yes. Men don't have any symptoms from having the hpv types that cause changes to the cells of the cervix, or abnormal pap smears. Men get hpv or genital warts caused by hpv types 6 and 11--then they will have symptoms of warts. If men have genital warts, they are at much higher risk of having other types of hpv that can cause abnormal pap smears for women.