First we need to agree on what’s meant by a ‘backfire’. Are your motors making bang-bang out of the exhaust, or out of the intake? True backfires come out of the intake / air cleaner.
Bangs from the exhaust are +usually+ the result of a rich, un-burned mixture igniting somewhere in the exhaust tract. On the other side, bangs from the intake are +usually+ the result of a too-lean mixture causing the motor to ‘spit back’ out of the carburetor & intake. And it’s generally normal for an older outboard to spit out of the intake a few times when it’s started up from dead cold.
Many older motors – not just outboards – have fairly crude starting devices, and they can act-up a bit when cold. If you can narrow this down, people will have a better idea of what to suggest.