Prior to being the prez at our school, we didn't have a Hospitality Committee. There were no drinks, snacks or munchies. This is one of the first things I initiated. Never having had one before, I wasn't quite sure what their job should be, so here is what I did:
The Hospitality Chair is in charge of providing snacks and drinks for each meeting. A budget of $10 is provided for each meeting. Our Chair provided fruit snacks ($1.50 at Walmart) and punch ($.99 at the local grocery) for the baby-sitting area. She also provided, from the $10, drinks (usually 2 or 3 grocery store brand soda pops in 2 liter bottles for about $1 a bottle and small, individual Hostess/Little Debbie cakes from the bakery outlet in town, with a cost of about $3). Napkins and cups and stuff we usually have on hand from earlier events.
Our PTO also balked at the $10 budget. Several of our members work in grocery stores and offered to ask their managers if they would be willing to provide the snacks and drinks for our meetings. Two stores agreed and now they trade off. Our Chairperson is still responsible for the coordination of the committee. Our Chair is also responsible for making sure all new members/visitors are greeted if the prez/veep are unavailable (when you gotta go you gotta go...lol). He/She also sets up and cleans up (or sees that it is done by someone else) the snack area.
The only other thing that might be included in their duties at our school, might be to get and collect and then run the door prizes.