We would just drop the roller setup into the 5 gal bucket with the paint, then cover the top with plastic, wrap with tape and you're good overnight. We always washed latex brushes every night. Our brushes were 30 to 40$ so you like to take care of them. I feel like a brush left in the fridge over night handles a little different then a fresh one. You can't cut in as fast or exactly. Sometimes we would switch brushes at lunch. I'm really picky with brushes though.
The longer a brush sits in paint, the more that paint wicks up the bristles towards the ferrule. One way to slow this process is to start with a wetted brush.
If painting latex paint, soak your dry brush in water before starting, and then hand spin the water out. There'll be enough water high up in the bristles to keep the paint from getting too high up there.
If painting with oil based paint, dip your dry brush in mineral spirits and squeeze out the excess before dipping in paint. Same idea as above.
Wrapping tight to keep in the moisture in is good, but I would not recommended putting it in the refrigerator. Keeping the paint cool should have no effect on keeping the paint wet. In fact, your refrigerator is a very dry environment, so putting it in the refrigerator should only make it dry out faster.
Yes, I actually paid attention in physics class.
Your refrigerator is actually a very wet environment. It may be low in absolute humidity, because the low temperature supports very little moisture content, but that is why it is always near 100% relative humidity. The RH is what matters when it comes to evaporation, and is why your crisper doesn't dry out lettuce and vegetables. But when it comes to latex paint, freezing will cause separation (i.e. putting it in the freezer will be a disaster), and chilling a few degrees will have almost no effect in preventing evaporation in comparison with just wrapping tightly in plastic.
For oil based paint, the cold of the freezer will significantly reduce the vapor pressure of the solvent, and significantly increase how long a brush can be left there. I've gotten many months this way with disposable brushes (I still wouldn't leave a good brush more than a week or so).