Sure, it can be done, but there are some things you need to think about.
The main issue is you won't be able to contact the arduino directly through the hotspot. This is because typically such hotspots do not give you a fixed IP address, by default. You might be able to pay extra for your wireless carrier to give you a fixed address for the hot-spot, and in turn configure the hot-spot so it can pass through packets for a particular port to the arduino. A more typical way to do this is setting up a control at a host with a fixed IP address and a web server, and have the arduino contact that. That host would act as an intermediary, relaying commands from you to the Arduino and back and forth. Presumably you would need appropriate security, etc. This means programming the intermediate host as well as the Arduino.
Given the limited memory in the Arduino, you likely don't have the resources to open up a VPN (virtual private network), which would allow you to contact the arduino directly.
Another issue is how much traffic is generated. While mobile hotspots/cell phones can give you the internet anywhere, if you exceed the data limit, you might get cut off, start paying by the megabyte for overages, or get your bandwidth reduced. If you are just sending text status messages every so often, that is probably fine. If you are trying to stream video, that will likely put you over the limit. Another issue is making sure you lock down the connection so other people don't start using it as free wifi.
Obviously your drone might have to deal with areas that have limited cell reception (dropped calls, no signal, etc.)
Finally, you will need to power the hot-spot, the drone, and the Arduino. I suspect the drone will use the most power, but you do need to take into consideration the power usage of the mobile hotspot.
Now, depending where you are in the world, and what cell phone company you use, rather than using a mobile hot-spot, you can get a GPRS/GSM Shield, which provides the mobile internet connection.