I've seen clear sunny skies outside of the city, but everytime I enter, it's foggy.

Is this a glitch?

It's usually foggy inside the city on my game as well. So I think it's intended. The same with all of Falkreath and most of the reach

Yeah, same thing in the Reach usually for me too. It's weird that right outside Riften it's clear and sunny and soon as I enter the city it's all foggy. Will the Clear Skies Shout get rid of the fog?

It's often foggy and cloudy, but there have been sunny days. Personally I wouldn't mind if there was just a little more sun in Skyrim as a whole so I wouldn't look at the glorious sunlight and be amazed by its rarity.

No sure I never tried it to be honest but I'm pretty sure it could work

I just read up on it and it says it clears fog, mist, snow and all. I don't have that Shout yet. It'll probably end up as one of my favorite shouts.

Or, if in a hurry to see clear weather, you can use a Console command like "sw" to Start a Weather change or "fw" to Force a Weather change.
From within the game, open the console by pressing tilde "~" (below the Esc key on a PC keyboard), and enter either appropriate command followed by a space and then the proper 6-digit weather ID. Then tap the "enter" key.
If interested, here are a few you might want to try:
10d9ec - SovngardeClear
10a7a5 - SkyrimClearVT
10a244 - SkyrimClearSN
10a240 - SkyrimClearTU
10a23b - SkyrimClearFF
10a237 - SkyrimClearRE
10a234 - SkyrimClearCO
10a230 - SkyrimClearMA
10e1f2 - SkyrimClear_A
10e1ee - SkyrimClearTU_A
10e1ec - SkyrimClearFF_A
10e1ea - SkyrimClearRE_A
10e1e8 - SkyrimClearCO_A
10e1e6 - SkyrimClearMA_A
10e1e4 - SkyrimClearVT_A

I imagine that the environment in the south is similar to the Pacific Northwest. Cold and rainy or cold and cloudy. Not enough sun in the summer or snow in the winter.

I think it's intentional due to an NPC referring to Riften being foggy most of the time but not the rest of the hold.

It is because of Elder Scrolls Lore. Riften is foggy/misty city and even the name of the keep is "Mistveil".

I was able to clear the fog in riften with clear skies shout.

Thanks. Looking forward to getting that Shout. It was sunny a couple times inside Riften earlier earlier in the game, but not anymore.

While normally misty I have had a few stunning, sunny days inside and outside Riften. Such a rarity though I thought it was a glitch at first!

I enjoy Riften due to the mist. You wake up in the morning and the droplets of dew are on everything, glistening and sparkling as morning arrives. Butterflies swoop down on railings for a drink before fluttering off into the nearby woods. Fires crackle as townsfolk huddle for warmth, wrapping their cloaks and fur lined jackets around them to keep the moisture at bay. Puddles form for birds who flap their wings while taking a bath. The rest of the moisture simply drips down through the city, into the lower levels and undercity passages. It's really well done.

The weather shouldn't change inside and outside the city since it's supposed to be in the SAME place. That is a bug or a bad design unless the city is in some pocket dimension of time/space. Going from one side of the city gate to the other should not affect the weather pattern.

@Kent Exactly. Is this a bug?

Its the scripted nature of the weather. Its kinda pathetic at times, you can run up a road in a blizzard, cross over the crest and be in full sunshine 1 minute later without moving any further. Backtrack on the same road and its a blizzard again after one minute. Run back up the hill and its sunny again.

Its things like this that take the gloss off the game. Weather should be identical inside as it is outside a town.