We are traveling to Innsbruck / Alpbach in the 1st week of March 2019, and would love to see some snow covered mountain peaks without actually having to ski, is it a possibility?
Depends how good you eyes are. :) I'm quite confident you will see snow-covered peaks in that area, although maybe in the distance. If you want to see snow close-up...that might require either good luck (depends on what kind of a winter they are having) or getting a bit up higher (or both). In early March, I think snow won't be hard to find.
Early March is still winter. You will have no problem seeing snow.
The weather can be erratic in times of global warming.
Here is snow for sure all the year:
https://www.kitzsteinhorn.at/en
https://www.hintertuxergletscher.at/en/home/