Here are some things you can do to keep riding safely through the Spring:

Wear functional clothing.
Use layers for easy stripping, in case you overheat. Or bring an extra layer to put on later. Avoid cotton, as it will trap your perspiration and make you feel clammy. Wool and performance synthetics are good choices. Select a good, wind-resistant shell (or waterproof suit, if you plan to ride when it's wet) as your top layer. In surprisingly cold weather, use windfront tights, or loose-fitting wind-resistant pants over your tights.

Protect your extremities.
Your fingers and ears might get cold once you get going fast enough for the air to rush over them. Or the wind might shift from the north. In any case, you'll be glad once the sun goes down that you brought your gloves and a light hat with you.

Be seen.
Front and rear blinking lights are the most effective and economical way to be seen at night. Stay away from dark clothing, or use a reflective vest.

Get good tires.
If you'd rather not sit on a curb and waste perfectly good warm, sunny weather while you fix a flat, invest in a set of high-quality, puncture resistant tires. There is no tire that will improve handling on glare ice, which you may still find lurking in the dark. However, there are tires specifically designed for better handling in wet or muddy conditions. When you go to purchase your tires, make sure you explain your riding needs to the salesperson.

Protect your bike.
Install full front and rear fenders, and clean and dry your bike after a ride through mud, deep puddles and residually salty streets. Don't let the goop stay on the bike too long. Lubricate your drivetrain frequently throughout the spring season, with a lube made for bicycle chains.