Most dogs shed fur all year round, but with the ones I've had, it seems that they lose more in the approach to summer, but I don't think that there is a major difference in the thickness of their winter fur in most breeds.
Beagles are bred go be hardy outdoor hunting dogs, who can go through muddy ditches, thick hedgerows and up and over gates when necessary.
Their busy time of the year is usually winter, where they run in a pack for mile after mile, over hill and dale.....whatever the weather.
However, if you have a beagle as a house pet, then probably he/she isn't "worked" at all, and therefore shivers because it is basically hanging around outside in cold weather. Any short haired dog would feel the cold, given the same circumstances. He's bred to be a toughie, but needs a fox to chase to get the blood going.....and a pack to snuggle up with in kennels at night.
If you seriously think that he is cold, then it would be probably a good thing to explore the net in order to find a suitable coat. The well known auction site has loads of sellers with such stuff.
One tip though......don't get a pink one, or one with ribbons, just in case he bumps into a pack of his brethren out there in a muddy field one day.