The Movie Timeline - be obsessive, be very obsessive
Where Eagles Dare - timeline
The briefing at the start mentions that the General they're rescuing is one of the planners of the Second Front. This was Operation Overlord, the invasion of Normandy in June, 1944. That places the film a few months or so prior to June. They land in a high alpine pasture that is abandoned for the winter, which means it's probably January or February at the latest, if it's 1944 at all. Given that they say a failure could result in 'no second front this year', it's probably early 1944. (Somewhere in Bavaria, Germany. The castle used was in Werfen, Au)
November: 2 secret agents (one British and one American) slip behind German lines on a mission to find a German double agent. (German Alps, Germany)