In 'Game of Thrones', the northerners believe that the Others (the White Walkers) are "
cold dead things, hating all life", or so it says the Old Nan.
On the other hand, the author GRR Martin says in an interview that they are not dead.
Spoiler of the 4rd season:
So, being believed to be dead by the northern folklore, the picture
should be accepted. However they are relate to the undead as they create undeads because the people they kill are converted into wights.
The horse is definitely dead.
