Dracula (and vampires in general, according to folklore) is not able to cast a shadow or a reflection. However, when Dracula first appears to Jonathan Harker (around 10mins into the first episode), he casts a shadow from the balcony in his castle.
Dracula is supposedly unable to cast a reflection, but he is reflected quite clearly in the varnished veneer of the dining table in his first scene.
In the aerial view of the horse drawn carriage taking Jonathan to Dracula's castle it's obvious the roads have been cleared by a snow plow.
Traditional folklore states that only the master of the house can invite another in to the house. A guest can not invite another person in to a house that is not their own.