So I understand it is possible to use an external hdd for gaming at the cost of speed. In what way would this slow down the game? Also if I had a 3.0 usb port would the difference still be noticable?
The game would take longer to load and it would be slower to load maps/levels.
SATA 3 speed: 6.0 Gb/s, USB 3.0 speed: 4.8 Gb/s, SATA 2: 3.0 Gb/s, USB 2.0: 0.48 Gbps
If you are getting a HDD just for gaming, then consider an SSD. It's usually 10x faster than a HDD. Get an internal one which has SATA III in order not to bottleneck the SSD's speed.
If you will get a HDD, however, get a USB 3.0 though.