Car won’t start. Could it because of the snowstorm?

It's highly doubtful.

When you say failed to start - did it crank over and just not start, or did it just do nothing at all when you turned the key.

 

Turned the key?

 

Turn on the headlights and see if there bright. If not you have a dead 12 volt battery that's in the trunk on the passenger side.

Battery is probably very old.

 

Cold Temperatures can affect a lot of things.
Most notably a 12 volt battery that might be weak.

On a Prius, the 12 volt battery doesn't crank anything. My understanding is that the 12 volt battery boots up the system, and the HV battery actually starts the engine. 12 volt boots up the system. The Prius doesn't have an alternator, and the 12 volt isn't used to start the engine directly like a regular internal combustion engine vehicle, so you sometimes don't get the same warning..slow cranks, that you would get with a regular vehicle.
So it would be helpful to know exactly what you mean by not starting.
Is anything booting up?
Other symptoms as asked, like dim lights?

My first suspect would obviously be the 12 volt battery. But it could be anything from fuses to a loose connection to some other as of yet unknown.

 

Only some Priuseses have the fancy cloud-enabled cordless witchcraft key. Some still use a cut metal shank with twisty requirements.

 

I think that's exactly what the dealership called it on my window sticker when I bought my Honda Fit.
It was right below the Amazing Outdoor Environmental Interaction Portal (Sunroof).

Seriously though in 2008 weren't the majority of all Prius push button start?

 

All true, except for the “c”.

Guess what @dubit has?

 

lol - I forget about the push button gizmo you all have sometimes

 

Which is why people should stick to their own forums, unless they are 100% fully confident in their knowledge of the Gen 2.

It gets quite tiresome correcting incorrect advice.