I had a FRA overnight in May. I went into town to save some money, but in the end decided I would have preferred staying at the airport. It was quite a long walk to the train track; I found it confusing signage as to which was the track into Frankfurt and which was the long distance track, and in the end the train to town arrived at a different track at the airport than scheduled.
Once I got into town, I was staying at a hotel just a block or so from the train station. Again, I found it confusing leaving the train station. Several of the exits were stairs, with no elevaors or escalators, so I had to carry my suitcase up them. It wasn't clear which street my hotel was on. In the morning I took a taxi to the airport. It was much simpler and faster.
In January, the midst of winter, I'd go for quick and simple - and that would be staying at the Airport Sheraton.