yes. 
Some engine designs  robbed cold start ability to  gain  upper end  horsepower/efficiency.   You could only do 'so much' with mechanical injected systems in regards to  nailing down  perfect  cold start  fueling.

Some are  dealing with  worn components.

Some  are dealing with  slower crank speeds;   either from  poor  battery/starter   drag on engine from parasitic  downstream ice cold  pumps/drives