If the engine cranks over normally (after a few rotations of the prop by hand - keys out, of course), the problem is unlikely to be battery related. Weak impulse magneto, inefficient primer, the engine cranking slowly due to cold, thick oil so that the impulse mag fires at the wrong moment, poor fuel vapourisation...how I wish we had aeroplane engines as reliable as my Honda VTEC!!
For some odd reason our 161 Warriors are often pigs to start compared to the 140C Cherokees; considerable priming and coaxing being needed to get the little $ods going in cold weather. Whereas I never had any difficulty with the injector-carburettor fitted to the IO-360 in the Bulldog, hot or cold.