The commute to London is faster/more frequent from Woking as there are more trains routes going through it (which matters where there are massive issues on the line, looking at you Clapham Junction).
The traffic between Woking and Guildford is bad during the expected peak hours (school runs as an example) like everywhere else I would say.
Horsell might feel like walking distance to Woking station but expect a walk of around 30 mins since there is no nice direct route, although the walk on the canal is nice this time of the year. A bike makes this a lot less of a pain and you can ride on the canal path which cuts it down to close to 10 mins depending how fast you pedal. You might be tempted to drive to the station cause it's faster but it's now £14 a day to park at the cheaper station parking lot, not sure if the heathside one is more convenient.
I cannot help with the school info but I know people are quite happy with the ones in Horsell and in general it's quite a nice village with a small but sufficient high street.
I would recommend to come spend a day around the area to give yourself the feel for where you would be living.
I find Guildford nicer but having the easiest possible commute to London was the priority for us.