1

Its not really just to do with height it depends on the weather running up to that time, the year i lived in Austria by May there was no snow left as high 1800 metres, but it was a bad year for snow, this year they have had large amounts of snow in Austria/Bavaria, so in May it could still be tricky above 1000 metres but at the same time there could be an early warm front.

2

My experience with mountain hiking holidays: all of your questions will be answered when you arrive. The most efficient thing to do is to be flexible with plans and alternatives. Don't lock yourself into one and only one alternative.

Snow conditions might keep some refuges closed until June, for example, and this might affect where you overnight. In addition to the point about weather conditions in the month leading up to your trip, there is also the matter of weather during your trip. Routes, even if clear of snow, might be fogged in on any given day making them unsafe.

So it all depends on where precisely you are and what the situation is like on the specific day.

3

It's partly a matter of altitude, partly a matter of exposure.
In the Bavarian Alps, you may be reasonably sure only by late May that the mountains below, say, 1700m are free of snow. Sunny southern slopes may be clear (and remain clear) from mid-April in such altitudes but in many years you may encounter snow in north-facing forests till mid-May even below 1400m, particularly if there has been a lot of snow that year. In January and February 2013, the amount of snow has been somewhat above average but that tells you very little about the amount of snow left in May.

I agree with the posts above, it all depends on the local conditions you encounter upon arrival. Locals may be able to give good recommendations on what to do and what to avoid - especially refuge staff (whose advice should always be followed). On the majority of sections, Maximiliansweg is technically not very demanding so that "some" snow should not be a major obstacle there.