The principle is to match the load carrying capacity. Then if you can, match the spring rate of the tire by using the same inflation pressure so the suspension reacts the same. (Yes, in spite of the fact that an uninflated tire may feel stiffer, the inflation pressure stiffens the tire way, way more - to the point where you can ignore it - except for ride quality.)
Usually winter tires are sized such that they have the same load carrying capacity as the "summer" tire, so the same inflation pressure would be called for. Let's see if that is the case here:
A P205/55R16 SL has a Load Index of 89, and a P195/65R15 has a Load Index of 89 - the same. So the inflation pressure ought to be the same. Sharp eyed readers will notice I specified the TRA (Tire and Rim Association - the US standardizing organization) sizing system (the letter "P"), and not the European or Japanese system (without the letters). For practical purposes, the systems are the same, and it was just easier to stay within the same system. Switching back and forth doesn't really change the way the tire is built, just the way its load carrying capacity is expressed, and there can be some minor - but confusing - differences.
Please note: When up sizing or down sizing (changing the wheel diameter), 2 things ought to happen: The overall tire diameter shouldn't change much, and the Load Index shouldn't change much either. The net effect is the inflation pressure shouldn't change much. EXCEPTION: Sometimes, upsizing results in a tire size without enough load carrying capacity - and in that case, usually the tire needs to go from SL (Standard Load) to XL (Extra Load) and you have to add 6 psi.