DO THE LAW OF PHYSICS NOT EXIST IN ICELAND!!
Well, in Phoenix, if there is going to be snow, it will either be on Christmas Eve or Christmas Day. Kind of a small window.
However, seasons there are easy. They start with June, July and Aug. being summer. Then Sept., Oct. and Nov. are fall. Dec., Jan. and Feb. are winter. Then March, April and May are spring.
Swim season is typically mid-April to around the first week of October.
Iceland has a traditional calendar which defines the first day of summer and winter in its own way. See http://www.icenews.is/2009/10/25/welcome-to-the-icelandic-winter/:
"... Iceland recognises the first day of summer as the first Thursday after the 18th April and the first day of winter as the Saturday between the 21st and 27th October."