Air carrier First Officer reported the flight crew went past the hold short lines due to miscommunication with ATC; poor visibility; and unlit holding position markings at the airport.

Narrative

Landing [Runway] 16 in HPN weather was very low; 2200 RVR. Upon landing we were told to roll to the end; and we did very slowly in the interest of safety. After acquiring the centerline; we notified Tower we were clear of 16. Tower instructed us to contact Ground 121.8;" I read-back "121.8." I then contacted UNICOM for a gate assignment; response was muttered and hard to understand. I then contacted Ground; then called again after no response. I checked the charts and saw the frequency was 121.82. After being heads down for a moment acquiring and dialing the frequency; I look up and start to make out hold-short lines. I say to Captain; "I think that's the hold-short line." I was too late; even with Captain's quick reaction we stopped about 4 feet over the line for [Runway] 11/29. I notified Ground and she instructed us to cross. The rest of the flight continued as normal.Cause: Low visibility; miscommunication with ATC; unlighted holding position markings.Suggestion: While we are at fault for this; I believe some things could have prevented us from making this mistake externally in low visibility. Tower could have corrected my readback; or the holding bars could have been lit for better recognition. For me; I could have notified the Captain that I was heads down. I could have asked Tower for a proper frequency."