Pickpockets are less of problem in January anyway as a person wearing a coat has many more pockets and it is difficult to see or reach the one with the loot.
This thread offers a few observations. One is that Rome and major other Italian sites have a problem with pickpockets, more so than other places. Sadly this is true, I've lost 3 wallets over the years, although not in Rome as it happens. I've been in Italy for the most of a year in total on multiple trips and I am not at all "bewildered and out of my element" there. I do not quite look Italian, but it is famously a country where people note differences in appearance and I do not think you can fool criminals easily .
There are two main approaches suggested on the thread, vigilance and keeping most of the good stuff out of the way. Vigilance has its own price, if you are spending your time watching your valuables, you spend less looking at Rome. These crooks are world class, and have a 100 strategies to relieve you of your possessions, unless you are trained you could hardly be vigilant enough. The last time my wallet was taken I would hardly have believed it possible, I knew who had taken it but couldn't do much about it. I very much favour the moneybelt approach, I have a cheap wallet, I put enough money in it for the next transaction, and if someone steals it I am down €10, but it doesn't bother me in the least.