I have ridden a lot of marginal roads and trails this year (T3-174) trying to get to better riding. If the snow is packed hard enough that you barely leave tracks you won't make it far without packing the tunnel with snow or doing something to help cool down. Generally it's not that bad and doing that 1-3 times gets me through the worst of it. Unless the snow is the driest and lightest of powder, just 1/2" of powder is good enough to keep the temperature good if the speed can be kept up enough that the snow actually gets on the cooler. For slower going, you might need more depth to get the job done.
I also load the track up with snow to help cool and lube it and the hyfax (mine are still in great condition) until we get to better going. Snow conditions this year have been a nightmare much of the time, but all in all it hasn't been a horrible job to deal with the cooling issues. Also, the air temperatures have generally be well above normal, which hasn't helped the cooling.
My opinion is if a person doesn't want to monitor and deal with it, don't get a 3". If some occasional extra steps won't bother you, the 3" isn't so bad and will give you a lot of extra traction when you need it. It would be nice to not have any issues, but reality is what it is. For every upside, there is usually a downside of some sort that comes with it.