Is it possible to install a new HP Envy-4520 printer on a computer running Snow Leopard

According to Apple's archived support article for supported printers, the ‘HP ENVY 4500 e-All-in-One’ is supported by Mac OS X 10.6.8. I recommend downloading and installing the most recent HP Printer Drivers (v2.16.1) for Mac OS X v10.6 Snow Leopard and see if the printer drivers for the HP ENVY 4500 e-All-in-One will work with the model you have.