There are plenty of small airports dotted around. The main issue that you will have is finding a small airfield that has both entry and exit custom facilities.
I fly from LSPN (no customs.) Its abt 1 hr from Geneva. Now that will test yr landing / take off skills - LDA / TORA 395mtrs
Not all mountain flying requires skis - I recently flew to LSZS (it supposed to be the highest airport in Europe - 5600ft above sea level) Approx 1800mts of tarmac and 2kms from San Moritz!