Funding
Most college teams are self-supporting; i.e. they raise a good part of their travel expenses through fund raising activities organized by the club, and pay for the remainder out of their own pockets. Contact your club sport supervisor for ideas. Many teams have had good luck hiring a professional fundraiser out of the yellow pages.
Most new teams will not get university funding for many years, and even then find it hard to get by on the money they receive. Of the non-varsity teams that are funded by the college (some aren't funded at all!), approximately $1000 to $2500 might be an average level of funding -- if you were to approach your college with a proposal, this would be a reasonable request. However, well-established and successful clubs earn as much as $15,000 in annual subsidies from their colleges. Varsity teams may get much more!
Unless your team is a varsity sport (and sometimes even then) riding is an expensive sport for those students involved. If your team is active, growing, and successful, you can usually get some money from the department or through student government allocations to student organizations.