A toddy is almost always a hot drink, if made cold, it would be hard to distinguish it from a sling.
Traditional recipes consist of a spirit, mixed with hot water and a sweetener of some sort. Sometimes it is garnished with a lemon twist or even a lemon wedge, and a sprinkling of nutmeg or cinnamon.
If you try to get a clear definition of the Toddy by using the Jerry Thomas Bartenders Guide, you will find it all quite confusing. He lumps the Toddy and Sling together, appearing to indicate that both can be hot or cold, with the only difference being a Sling is server with a grating oh nutmeg.