Want to install OS X snow leopard from disc onto external ssd drive

The first order of business is to boot from that Snow Leopard disc. To do that insert the disc and hold a C key while the Mac starts up. That causes the operating system to boot from the optical drive.

If that does not work hold an Option key while starting the Mac. An array of icons will appear with eligible startup devices. The Snow Leopard DVD will appear as a silvery "disc" icon.

One way or another, boot from that disc, select the option to install OS X Snow Leopard, and choose the external SSD as its installation target.

This assumes the SSD has already been formatted. If it has not, then you need to choose Disk Utility from the OS X Utilities menu and format the external SSD. Choose Mac OS Extended (Jounaled) as its Format and GUID Partition Map as its Scheme. Its name can be anything you choose but the usual name is Macintosh HD. You may want to choose a different name if that's already the name of the iMac's internal hard disk drive.

You will need the gray Restoration DVD for the 2010 iMac since I don't think a retail upgrade DVD will work since the 2010 iMacs shipped with a slightly later 10.6.3 build than the retail upgrade DVD. Unless of course there is a retail OS X 10.6.4+ upgrade DVD out there (I don't think so).

Plus with that older OS, you will need to partition & format the whole physical drive. Here is an article with instructions to do this:

https://eshop.macsales.com/tech_center/formatting/Mac_Formatting_6-10.pdf

Unfortunately an external macOS USB drive will be extremely slow due to the USB2 interface which has a max transfer rate of about 45MB/s. USB2 data transfers were not very efficient either which makes USB2 even slower for a boot drive. An external FW800 enclosure with your SSD would be much better.

It's not clear to me exactly which Snow Leopard disc you're using. If you can't boot from it then either it's not a boot disc or the optical drive has failed in some manner.

Any Mac that shipped with those grey discs must retain them from cradle to grave. They were not copy protected meaning they were copyable with suitable software, and if you lost those discs Apple provided replacements for a while. They were white discs with plain text markings. Those days are long gone.

The other option is to find a retail, white, Mac OS X Snow Leopard Install DVD with a picture of the big cat on it, but as HWTech wrote I cannot be certain it will work with that specific Mac model. There were no such discs with any later OS X version than 10.6.3. They remain available on a popular auction site at reasonable prices, so if you find one, I recommend you buy it even if you're not 100% certain it will work.

The standard procedure would be to boot from that disc, install that OS X version (on a device that works), boot from that device, update OS X using Software Update, which provides OS X 10.6.4, which provides the App Store, after which you can update further if you so choose. But the first order of business is to boot that Mac from that disc — or one that will work.