There is no rule that a campaign world must conform to the physics of climate as we know them here on Earth (for that matter, who says we know them here on Earth IRL? The Weather Service is only right half the time about the weather forecast for tomorrow.)
If your world does not conform to our climate physics, that does not mean magic is necessarily the culprit in the different climate ... perhaps, the climate is what it is, and nobody knows why.
Remember that the concept of Warm Fronts and Cold Fronts, High Pressure and Low Pressure, were 20th Century inventions.
The Horse Latitudes were discovered by mariners during the Renaissance, because in the becalmed conditions the men on board went hungry and ate their horses to survive (or threw them overboard, one of the two. At least, this is the fable I've heard!)
The Doldrums, that area of constantly rainy weather that fluctuates back and forth across the Equator, was also discovered during the Renaissance.
(Yes, the native peoples in the tropics knew all about both of the above since time immemorial. I am referring to the Europeans here.)
The Jet Stream was discovered during World War II by bomber pilots who discovered themselves barely moving when at full power, or flying along at far greater speeds than they had expected.
The Circumpolar Vortex and other climatic things of this sort were discovered and named in the latter 20th century.
So, if the people of your medieval world speak in terms of warm fronts and high pressure, the jet stream and doldrums, polar vortexes and horse latitudes, they are unlike the Europeans of old!
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Here is an example of a popular world that has a very un-Earthlike climate: Darkover.
On Darkover, the climate is a variant of arctic.
During the summer, temperatures warm up during the day into the comfortable range - perhaps turning even hot - then drop quickly at night to well below freezing.
Sometimes it will rain during the day, with the rain turning to snow during the short night.
Sometimes, it will turn unusually warm, and nighttime temperatures will stay above freezing - when this happens, watch out, for some of Darkover's more exotic plants come out and bloom.
And sometimes, raging blizzards and frigid temperatures occur, even during the day.
Winter is COLD. Even at sea level, even near the equator. By cold, I mean Siberian cold. Unrelenting, monstrous cold.
Yet in spite of all this, great forests of frost resistant trees and plants grow on this world, great harvests of adapted plants are reaped, and large numbers of humans live here.
Another place with a vast temperate climate is Tolkien's world, Middle Earth.
The temperate range is truly huge. The Shire has a temperate clime, and so does Gondor. The Iron Hills are temperate, and so is Mordor (well, at least, those places in Mordor where climate means anything.)
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It is my opinion, for what it is worth, that a world in a mild to moderate ice age could have vast temperate regions and few tropical regions.
Why? It is rather simple, really.
The large icecaps in both hemispheres - and there will be, obviously, large icecaps in an ice age - are very cold.
In Antartica today, in the real world, temperatures in the interior are below zero even in the summer, and can drop to 50 below zero.
During the winter, temperatures range from 30 to 100 below zero.
Now, if you have large Antarctica-like icecaps in both hemispheres, cold air will flood down out of them towards the equator, the year around.
During the summer, the sun and warmer seas will mitigate this cold enough to allow a summer to occur, with growing seasons and trees leafing out and so on.
But during the winter, the blasts from the incredibly cold icecaps will not be mitigated by the sun, and will only moderate once they have penetrated deep into the warm oceans near the equator.
Thus, the hemisphere in winter will be cold clear down to about 10 degrees from the equator, especially over land.
At the equator, a cold ocean and chill breezes will produce a constantly cool climate, never really becoming cold, but also never really becoming warm either.
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Perhaps your world has a much greater axle tilt than Earth.
I created a version of Krynn that had an axle tilt of 80 degrees.
This means that, during the southern summer, the sun shone all the time, and during the southern winter, the sun did not shine at all anywhere south of 10 degrees south (just south of the equator.)
Furthermore, Krynn was closer to it's sun during the southern summer, so the constant overhead sun was truly scorching in it's intensity.
During the southern winter, Krynn was much farther from it's sun.
As a result, the Krynn I created had an extreme climate in the southern hemisphere, where during the constantly sunlit summer the temperature rose to 200 degrees far inland, and during the dark winter it dropped to 100 below zero far inland.
At the equator, the climate was roughly temperate, with the hot season during the southern summer, and chilly (cold over land) conditions during the southern winter.
In the northern hemisphere, the weak, constant summer sun produced a pleasant, cool summer, while during the long winter night warm air-masses roaring up from the equator produced hurricanes, heavy cloud cover, torrents of rain - it was warmer in the northern hemisphere during the lightless winter than it was during the everlit summer!!!
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Any world that has a high axle tilt (say, 35 degrees, for instance) will probably have large temperate zones.
As the sun rises high in the sky, and beams down on the polar regions, the whole hemisphere warms up, and it is summerlike even at high latitudes.
As the sun goes down, and is scarcely seen, during the winter, all the land masses cool, the oceans chill, winter takes over over most of the hemisphere, and chill winds roar towards and across the equator.
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. It does only mean that the water is colder than the night temperatures in that region. Therefore, the rain goes down on the ocean, not on land, resulting in a desert.
