Why did Arwen go to find the hobbits?

[the phantom]

You can't have a zillion characters running around, and expect people to remember each and every one of them.

I'd remember them.

Plus Glorfindel is only one extra name, not a zillion.

And yeah, the movie did need to do things slightly different to develop the Aragorn+Arwen relationship- but with all the other Aragorn & Arwen stuff they did the FOTR horseback rescue was not necessary at all.

Liv Tyler looks hot on a horse.

I'll give you that.