Yes, there have been studies on how much various fabrics insulate when wet and dry. I remember Dr Murray Hamlet mentioning these statistics in one of his lectures on outdoor survival in the cold.
It's been a long time, but I think cotton looses something like 80% of its insulating properties when wet. I may be off on the exact number, but I definitely remember it is significant. Good cloths for this purpose were wool and polypropylene. They only dropped by 10-20% if I remember right.
That all said, cotton is still more comfortable, at least to me. You can wear cotton in the cold if you understand the risks, tradeoffs, and are prepared to deal with it getting wet. Dealing with it can include changing to other clothes you brought for that purpose.
For example, when hiking around town, I wear whatever is comfortable. I'm never that far from the car, and the conditions are predictable enough over the short term that the worst that will happen is I'll be a little uncomfortable on the way back to the car. That's often a risk I'm willing to take.
On the other hand, when hiking in the White Mountains of NH, I need to be more conservative. It can be miles to hike out or to the next shelter. There I usually wear a polypro sweater with a wool sweater over that and a windbreaker over that when going deep into the wilderness in winter. In that case, carry a few reserve layers too, including extra socks, balaclava, ski goggles, and usually a stove of some sort. You can't plan for every possible contingency, but I like to cover at least the situation of a twisted ankle several miles from civilization. It can be deadly if you just went out with a cotton shirt and wind breaker, then you twist your ankle, you don't get back when intended, it gets dark, and starts raining.