Hi Ed
Not everyone drains the oil cooler, in fact the manual does not even mention it, but the lines come down and connect to the engine right where the oil filter is, so for my machine, I loosen both lines and let them drain when I remove the filter. Pretty easy to do.
The downside is that if you damage any of the aluminium crush washers (there are 4), the lines won't seal again and you will need to replace the crush washers. I have done mine at least 8 times now, with no concern, but I will likely replace all four washers this spring, just to be safe.