I have a 50x23 rink in Massachusetts. The ground is pretty sloped so the water is about 4" at the shallow end and more like 18" at the deep end. The rink freezes fine, but I had a question about the ice at the deep end.

I've noticed that at the deep end the ice looks more 'wet' (its not actually wet - just the ice is a different color), presumably because there is water underneath. Whenever we have snow, the deep edges get the most slushy. I was thinking this was because the water was wicking out, or the weight of the snow was pushing up the water around the edges. The ice also seems to melt first at the deep end.

I was wondering whether the boards being exposed to the air at the deep end is not allowing the water to completely freeze - would insulating the boards help? e.g. putting a layer of that pink house insulation against the outside of the boards?

You're correct that when it snows, the weight of the snow pushes the ice down and water seeps up around the edges to create slush. It's not that the boards aren't allowing the water to freeze...it's just that it's very deep there. Think about a pond...if you go ice fishing, you might only have 10" or 12" of ice, as it freezes from the top down. Same deal with your rink...you have 18" of total depth, but maybe half that is frozen. It's been very cold this year, but the only way to really freeze all the way to the ground is by leveling your yard a bit to reduce the depth in your deep end.

for me it is the opposite as my shallow end gets more sun. Therefore it is softer and melts more.

Add topsoil to the low parts of your lawn and add grass seed. :)

FWIW I figured out what was really going on here.

Last year I built up underneath to make the water level around the edge such that it was frozen to the ground, and I still got water leaking over. Then I realized I did not have enough bracing - I secured the boards more firmly and magic - no more water flowing up onto the ice.

I seem to remember reading "you can never have enough bracing" on this forum - so true.