Wow! That's tricky! I'm not really sure there's any hope reading the reg number in all that fuzz, but I would say the birth year is 06. That's probably not very helpful is it? Sorry.
If I was going to have a crack at the rest of it, i'd say...648 for the first bit. Not sure about the last half....644? Sorry if that's all useless. It's really tough.
Maybe you'll see more in her summer coat.
Good luck working it out!
~The most important lesson my horse ever taught me is how much I have left to learn~