Cold weather and cold engines are often problematic starting whether it be Briggs or other, lawn mowers or snow blowers. My 48 Ford coupe was in that category but that's a whole different story and very long. Being the choke doesn't seem to accomplish much in this regard on my Briggs, I took it upon myself to determine a better way, than just pouring, to prime with gasoline.
In the picture we see an Echo bottle containing gasoline. Also between the bottle and an eye dropper is a visible stub of a 1/4" wood dowel ( tapered on insertion end ) inserted into a automotive valve stem butt. This valve stem is located directly above the carburetor throat and after the air filter. Schrader valve removed.
How it works: The eye dropper is kept in a paper towel sleeve for sanitary reasons along with the little bottle of gas stored in the tool storage area of the lawn tractor. To prime, remove the dowel plug and place it on the seat. Fill the eye dropper and discharge it into the butt of the valve stem. If the eye dropper only sucks about half full do it twice. Replace the wood plug. If you forgot, you felt it on your butt when you set down. That's why you put it on the seat. To start, choke engine fully and it often fires on the first compression stroke and keeps running if the throttle is about half or more.