Tethering is exactly as taxing as using the phone. If the device you're tethering is downloading a file, it's the same as the phone downloading the file. If the device is viewing a web page, it's the same as the phone viewing that page. (The tethering software, the hotspot, uses power, but saving a file on a tethered laptop doesn't use the phone's battery, saving it on the phone does, so it's about a wash. Same with viewing on a laptop screen with the phone screen off, or viewing on the phone screen.)
The only difference is getting into trouble if your carrier and your plan don't allow tethering.