Have a look
Choosing Family 1080 Camcorder
Budget camcorders tend not to be overwhelming compared to the quality we are all now used to with BBC/ Sky ect
Video quality is somewhat proportional to cost and it makes sense to buy what you are most able to afford.
£500 seems a decent sum but many camcorders will struggle with AF with the poor contrast of snow in snowboarding
The other challenges would be accurate white balance and exposure
As such Consider a model which has some manual control of WB and exposure modes
It is these features that separate the simple " memory makers" from Camcorders which are more able and therefore cost a bit more
The other issue is how fast motion is handled
Whilst awaiting suggestions I suggest you put on a few models and let owners or those who have used them chip in
Although Ive used a few of the newer models I relly still own MiniDv tape HDv models which serve me well.. so far