Don't put your bike away when the clouds are grey! For the cost of a couple of tanks of petrol, you can keep cycling comfortably through the seasons. Here are some thoughts on utility biking in the rain-
Water'll hit you from three directions- the rain from above, water splashed up from your tyres, and your own body -sweat and evaporation. So you'll need rainwear, good shoes, and mudguards for your bike.
Most cyclists in wet climates use a good rain jacket combined with over-trousers. The jacket is usually a rainshell without lining, so it can be used on mild days. Both should be waterproof, windproof and breathable. Often, the jacket or coat you use for tramping will be fine. Wear removable layers underneath - rain means humidity, so another option is to stay in a low gear and cycle slowly, to avoid getting to your job or your Mum's in a sweat. The alternative to jacket & overtrouses is a rain cape, which goes right over the bike from handlebars to your neck. Whichever you choose, get the best gear you can afford; think of all the petrol you'll be saving!
Normal good waterproof shoes should be adequate, but don't forget that rain will flow down those waterproof trousers over your shoes, while your tyres spray them from beneath, so they need to be up to the job. Boots can be a good option.
A good set of mudguards are a must for your bike. Bikes vary so much in gearing and suspension, it's often best to ask at your local bike shop about fitting. Think about whether you want removable or permanent guards.
To keep your stuff dry, waterproof panniers on a luggage rack are ideal, providing refuge for your schoolbooks and laptop in even the heaviest downpour. In a pinch, a plastic or ziplock bag wrapped round your delicate items and popped inside your basket, pannier or backpack will protect them. Hi-viz backpack covers can adding rain protection if you have to carry your luggage on your back.
Don't forget that people using cars in rain have their visibility badly reduced, so switching on your lights and donning hi-visibility clothing, even during the daytime, is a good idea. Keep your normal road position, about a meter from the kerb, and reduce your own speed so you can keep watch for puddles and slick metal plates in the road- your brakes & tyre grip will likely be affected by the rain so allow longer stopping distances.
Finally, cycling in damp weather with light rain can be OK, but heavy rain is another story; even the best rainproof clothing will struggle in a heavy downpour. Sometimes the bus is best!