@partyponies , Rebecca , If you are getting a spark and fuel to the carburetor and the engine cranking over on good, the problem is probably the electric choke or heating element for easy cold start is not operating correctly. When the engine is cold the choke is required to start engine correctly, If faulty, the mixture will be weak and the engine will not want to start easily. Have a good local shop check it out, diagnose and estimate repair.Links below may be of some help, 1st link is about troubleshooting and the 2nd link is a service repair manual not your exact year but may work. Good luck. I hope this helped you out, if so let me know by pressing the helpful button.
http://www.scooterfocus.com/scooter_troubleshooting.html
http://www.49ccscoot.com/manuals/Yamaha_Vino_125_Service_Manual.pdf