i would just like to know how you get enough people to form a committee? we have difficulty getting a quarum of 6. anyhow in answer to your question, anybody other than an officer is more than welcome to head events, activities, etc. problem is they rarely want to so the board does it.
short of digging out "bob's book" ... we don't encourage board members to chair committees, though it happens on occasion. kind of depends on how you define committee or which committee you're referring to.
i don't think there's anything wrong with a board member being on the budget committee. at the elementary schools we have always had treasurer as member of the budget committee and we usually have the Principal sitting on the committee as well.
what do you use your budget committee for? our middle school doesn't even have a separately defined committee as such. the budget is typically put together by the executive board (the treasurer brings the historical accounting records)-- we look at recommendations from committee chairs for changes, get some input from the principal..... then present it at the first PTO meeting of the year... it usually takes about an hour to beat the whole thing thru. Adjustments can be made, etc... and the budget is then approved by vote of the members present.