This is something that I've wondered for a long time, but just now thought about. Why is it suggested that if one encounters ice, that person should climb to a higher altitude. I can understand the idea of "more altitude, more options," but it seems to me that in any case other than a temperature inversion, temperature reduces with altitude. Seems icing would be worse if you climb. Any moisture that has not become ice would freeze (at least in my mind).
What am I missing?
a) Not a good idea unless your plane has a lot of excess power.
b) If it's freezing rain or freezing drizzle, you are (by definition) in a temperature inversion. That's the main origin of the advice. If you're in freezing precip and have a lot of power, it's theoretically possible to climb into the above-freezing air where the rain or drizzle is originating. But most of us don't have that much surplus power, and every minute your airframe is accumulating SLD icing, your performance is degrading, so soon you'll be struggling just to maintain altitude. If there's freezing precip (SLD) in the forecast at all, piston aircraft--and some turbine singles, like the Caravan--need to stay on the ground, even if they have FIKI.
c) If it's light rime (SSD) in a 2 or 3,000 ft layer of broken strato-cumulus (very common in late fall/winter/early spring around Ontario and Quebec), the rime-ice accumulation will stop as soon as you're above the clouds--generally at around 6 to 8,000 ft MSL in the regions north of the Great Lakes and New England--and will quickly sublimate off in the sunshine above, even if it's well below freezing up there. You usually pick up just a little frosting climbing up through the clouds, not enough to affect performance. But always have an out (or three) in case it's worse than expected, because weather has a way of sneaking up and kicking you in the behind.
Lake-effect icing in the lee of the Great Lakes with a cold winter NW wind is a special case. It will usually be severe clear above (tops out around 6 to 8,000 ft MSL again), but inside will be severe SLD icing and heavy snow. It's usually in well-defined areas, with streamers extended further. I've often overflown it between Ottawa and NYC in my PA-28-161 (mainly around the Watertown/Syracuse area), with severe clear on both ends, but like flying over mountains, there aren't a lot of options if you have engine problems while you're on top, so it's a personal risk decision. It's different from the normal freezing rain and severe SLD icing ahead of a winter warm front because it tops it so low and is usually clear above (winter weather ahead of a warm front can extend into the high teens or 20s).