Welcome to the STD forum.
"Relatively
commonCommon cold" understates the frequency of HPV. The large majority of sexually active persons get genital HPV, often several times. Most infections remain asymptomatic and never cause health problems at all. If you were infected, that's the likely outcome in your case.
The efficiency of HPV transmission -- i.e. the transmission risk for any particular exposure -- really isn't known. If indeed your partner has a currently active HPV infection, then it's a pretty good bet you were infected, but by no means certain.
Presumably your partner hasn't had a diagnosis of warts, only positive HPV by
papPap smear
Pap smears and cervical cancer smear. If so, the chance you'll get warts is low -- but not zero. Penile cancer is extremely rare, and is no more likely in you as a result of this event.
Bottom line: Don't worry about this event. Keep your eye out for penile warts in the next 2-3 months, and see a provider if something shows up. But there will be no long term health consequences and you don't need to tell future partners about this event.
If you will search this forum for "genital warts" or "HPV", you can find innumerable discussions that go into all this is great detail. Also look at the information available at www.cdc.gov/std and www.ashastd.org. After you have done that homework (but not until then!), feel free to return if you have one or two brief follow-up questions.
Good luck-- HHH, MD