I've thought sometimes about this possibility, but I've tried last winter the following shortcut (by car) : Nowy targ -> Czarny Dunajec -> Jablonka -> Lipnica Wielka - Bobrov –
Rabca – Korbielow – Bielsko Biala – Katowice.
Excellent if you live in the Slask region and want to avoid traffic jams on the Zakopianka !
For getting to the Eastern High Tatras I also often use the road from Nowy Targ to Podspady via Jurgow, far less crowded, and so much more practical and beautiful..
By public transports I didn't develop much the paragraph on this page, otherwise it would quickly become an encyclopedy :)