Here is an excellent guide:
The above is guidance by the UK government, particular points are very signifficant:
there is a small sticker for your car's windshield known as a vignette, it verifies that you have paid road tax ( I think the weekly one is 8 euros). You can purchase one at the border.
you need to carry evidence for your car's ownership and insurance
as you might know, your headlights must be on at all times, day and night
As stated by the European Commission here http://ec.europa.eu/transport/road_safety/going_abroad/bulgaria/other_en.htm
You must also have a warning triangle, first-aid kit and a fire extinguisher (small is fine) in the car, also just in case - a hi-viz vest.
And also there is the following legislation:
"Snow chains must be carried from 1 November until 1 March and used when the relevant sign is displayed"(first url).
Considering the weather there now, I would wear chains even on my shoes.