The snow conditions may vary from very minimum to tons of snow on the approach and in the MR gully. I have experienced both extremes during Dec climbs in the area, so watch the forecast and plan accordingly. The avi danger is usually low on the MR, I would definitely be more concerned about icy patches, especially as a soloist. The spots that tend to get slippery include Ebersbacher ledges on the approach (these are usually by-passed when there is enough slow covering the creek), a small wall right before the iceberg lake plateau and last ~400 ft, after you exit the MR gully. Depending on snow coverage and conditions, you may be able to sprint from the portal to iceberg lake in 4-5 hours, or will have to crawl for two days. Also, the portal road will be officially closed. Most people drive past the sign, but the chances are high you will have to stop at some point because of snow/ice, which adds a few extra miles to your approach and retreat.
Cheers