Edinburgh is on the east coast so it doesn’t rain too much, not windy every day, not very windy that often. Seldom very hot, doesn’t snow on many days each year.
If you don’t like the weather when you wake up, or the forecast for later, you don’t have to cycle.
Many people do cycle ‘whatever the weather’ – they tend to be ‘seasoned’ commuters and have good quality waterproofs and warm clothing – in layers. (Clothes page)
“I’d get wetter walking the 10 minutes to the nearest bus stop and then from the bus stop to work.”
There are many sites and apps to choose from. Some people like detail others just simple graphics. Recently (July 2015) “no rain” has been forecast for the next few hours, immediately followed by torrential rain!
This site shows current conditions and data going back several years – University of Edinburgh School of GeoSciences weather station (at KB)
Met Office, UK climate If you click on the averages map and select rainfall shows that Edinburgh is an ‘anti-oasis’ with only 1 in 3 days getting any noticeable rainfall.
This site often more accurate!
Given you aren’t cycling all day helps show that it is rare to be caught cycling in the rain.
Lighting up times in Edinburgh On dull overcast days it’s wise to have lights even if not legally required as dusk descends.