I live near Edinburgh, although I am English my children are Scottish having been born in Edinburgh.
The weather is generally worse here in Scotland than in England. Ignoring the localised flooding, then that has been the case for the last 3 summers which have been cool, cloudy, wet and windy. It is also generally wetter the nearer you get to the West side of the country.
It does not stop us cycling, but you have to take, or wear, clothing for wet, cold and windy.
I cycled to Dumfries for a 4 day cycling meeting at the end of May this year. I has a 90 mile ride there in a steady 25 mph cold headwind with showers, often of hail. I was cycle camping and it was hard going over 3 days. I was having to pedal down steep hills where you would normally reach 30 mph freewheeling and even had to get off and walk up one or two as the wind wore me down.
The four day event was very enjoyable, 1 very wet day and 3 nice sunny days. The country round Dumfries and SW Scotland is beautiful and made for cycling as long as you enjoy hills.
If you are planning to come here and cycle you will find the country roads very enjoyable, just avoid main roads where possible and make sure you have some wet weather clothing in case of rain.