The bleeding is probably more likely to be bramble/cover damage
Frostbite occurs when a part of the body freezes and it often accompanies hypothermia so really unless its minus 10 then most of our dogs are going to be OK so long as you do all the things that will prevent it
IE, cutting back feathering on legs feet and chest and bum to stop the build up of snow, using something to stop the snow building up ie baby oil, lanolin baby leave in conditioner
It tends to involve the tail, ear tips, pads of the feet, and scrotum. These parts are the most exposed and least protected by fur.
Frostbitten skin is pale white or blue to start with and the dog will feel pins and needles, throbbing and aching
but as circulation returns, it becomes red and swollen and may begin to peel.
(So if there tender parts or "their Nads" as they are known here remain healthy pink colour the day then you should be A OK).
Eventually it looks black with a line of demarcation between live and dead tissue seriously not good!
Dead skin and tissue separates from the body in one to three weeks which is why Sir Ranulph Fiennes
Treatment:
Apply warm (not hot) water soaks to the frostbitten part for 20 minutes, so under a luke warm shower is ideal til the tissue becomes flushed.
Never use snow or ice; tissue damage is made much more severe if thawing is followed by refreezing.
Do not rub or massage the affected parts.
Handle them carefully.
Take your dog to a veterinarian for further evaluation and treatment.
Note that as sensation returns, frostbitten parts can be painful.
Prevent the dog from biting at the skin and inflicting further injury. T
he total extent of damage may not be apparent for a week or more.
Hopefully even though we have had lots o snow the air/ambient temperatures have not bee that low to cause any damage