Alternate Seasonal Variations

Seasons are generated due to the differing incidence of light from a star onto a planet from axial tilt. As the plant revolves around the star the amount of direct vs. diffuse sunlight alternates between the hemispheres. For us, part of this seasonal variation is due to the shifting of the border of atmospheric cells (i.e. Hadley, Ferrel, Polar).

Okay, fine. If you had a planet with minimal axial tilt, you therefore would have a minimal seasonal change. Weather would be fairly constant, although you would still have variation from heat transfers between land and sea.

But, what if you had a planet with a minimal axial tilt and a relatively eccentric orbit? A planet with Venus' axial tilt and Mars' eccentricity- It would have seasons that would be based on a variance on total light exposure. This would make for a more planetary than hemispherical seasons. However, would you still have the full range of climates on this hypothetical planet? Could you have a tropical zone, or would you have a new type of temperate climate that has particularly dry, hot summers and wet, mild winters instead of a monsoon season?
 

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I think with an eccentric orbit you would get a world-wide monsoon season as the planet moves away from its star and the atmosphere cools. It may not last long (a few weeks?) and probably won't be simultaneous. Even at the poles, the Annual Regularly Scheduled Blizzard.
 

However, would you still have the full range of climates on this hypothetical planet?

Broadly speaking, yes. Seasons are variations of climate, not the originators of climate. Sunlight will still be nearly horizontal at the pole, so it'll be cooler, and sunlight comes straight down at the equator, so it'll still be warmer. The details - exactly how cold it is at the poles, how warm at the equator, and how wet or dry various areas are, will depend on the local details - positioning of seas and mountains and such. But you've basically just said that the North and South hemispheres experience their seasons at the same time, instead of alternating.

Now, there may be some oddities of atmospheric dynamics we are missing, and that the seasonal temperature variation pole to pole may drive some heat and atmospheric flow the leads to some weather patterns we think of as common. I'd need a simulation to be able to tell that.

Edit: Doing some quick reading, I'm finding a suggestion that axial tilt tends to moderate temperature, overall. So, if you lack tilt, you get much more variance with latitude - the equator is hotter, and the poles are colder as a result. In an extreme case, you can have gases boiling off at the equator, and freezing down at the poles, leading to collapse of an atmosphere.

This last I'd take with a grain of salt - we used to think similar things about tidally-locked worlds, until we got better models of atmospheric flow, which showed that atmospheric flow could moderate temperatures more than expected. I wouldn't be surprised if the general point still held - without at least 5 degree tilt providing variation, places tend to bake and freeze.
 
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