Asking for reimbursement for visa costs
Most universities have detailed "travel policies" that describe their rules for allowable travel expenses.  Try to find your university's policy; it may state explicitly whether or not visas are an allowable expense for reimbursement.

If you can't find the answer yourself, then it's certainly fine to ask whether this expense can be reimbursed.  I don't think you need to worry about this being seen as "special treatment".