Can I drill holes into the front of my fridge to attach a new handle?
It depends on the refrigerator, of course, but a typical sheet steel unit can take short sheet metal screws without issue. You'll want to be sure you don't penetrate any wiring, tubing, or the inner panel or seals.
I'd consider backing up the screws with the strength of permanent double-sided foam tape. Screws under regular strain tend to work loose over time, and the added stability this would provide would help prevent failure.