Saint John is located on the Bay of Fundy, so days can be surprisingly brisk, even in summer (54-70 F/12-21 C). Many travelers are surprised by how cool the wind feels, even though the temperature is warm. Occasional fog lends the city some atmosphere and makes it even cooler. Fog moves in fast and can take you by surprise in any season, although it happens most often in spring and summer.
Expect cool temperatures in the summer and always, always pack rain gear. Autumn usually brings pleasant weather until about mid-October, when things become chilly and damp. It isn't likely to snow until late December, but spring doesn't return until May.