As other pointed as well, from Delhi the route isn't very difficult NH1 is one of the nicest road around Delhi.
DELHI - SONIPAT - PANIPAT - KARNAL - AMBALA - LUDHIANA - JALANDHAR - PATHANKOT - JAMMU - KATRA
In Katra you can book the JKTDC Yatri Niwas which are pretty comfortable and adorable, it be booked online as well over here Untitled Document. Book in advance to avoid any issue when you reach katra. You may also book a cottage room up-hill near to vaishno devi mandir.
After arriving at Katra, do remember to pick up yatra slip from local travel office, near to bus stand which will be required up before the mandir. Ask anyone where can you get the "Yatra Slip" if you got confused anyhow. Katra - Vaishno Devi Mandir - Katra will normally take 12-13 hours to complete the journey comfortably. Being decemebr you wish to see the snow will fullfilled at Vaishno Devi Mandir only
From Katra you can visit Patnitop which is around 1-1.5 hr drive from katra. Another place to enjoy snow, but i would suggest to pre-book hotel before arrving.
Last but not the least, Jai Mata Di |