In regards to cold starts on these, it is best to remove the air box to confirm that choke plate is shutting fully and actually opening when the engine starts. Some LTs with the CV series engine had this choke wizard that was spring loaded at the top of the shaft rather than a solid choke shaft. The other item of contention is the mechanical fuel pump. Once could remove the bowl and crank the engine and see if fuel is pumping as the engine is being cranked due to the low RPMs. It gives a look too that you have a bowl that is half full of fuel or not.

OP: I don't know if it was happening or it was my imaginations, but when I tried to cold start, the starter seemed to run longer than it should when the key returned to its normal position. Could an ignition switch malfunction cause hard starting?

since the engine started on the ether, the problem is probably not related to the ignition system. Fuel in the carburetor float bowl has probably evaporated and the fuel pump is not able to replenish during cranking speeds. Air is drawn in the fuel line - probably around clamped connections around the fuel filter or the connections to the fuel pump. Is this a pulse pump? The pulse line to the fuel pump may have deteriorated. some of these had a rubber bushing on the valve cover for the engine breather. When these connections deteriorated, the fuel pump may not receive an adequate pulse at cranking speeds. Old fuel may not vaporize easily. Neither will summer fuel exposed to colder temperatures. Ethanol fuel may contain some water. Low engine compression can be a factor

good suggestions from tomplum.

A dealer should recognize most of the issues mentioned.

I would go with Tom,s advice appears to be a Cold Start no choke situation . Check choke plate when engine is cold to ensure it is closed fully upon start up . Also ensure clean fresh fuel always and as advised float bowl is full , drain plug will help determine fuel is in bowl prior to attempting to start unit .