Does the speed reduction affect all speed or only walking speed?

It would be all speed

Casting Spellword is: Dartus Freezium

Eazy Squeasy Legsy Freezy

It only works on creatures. Therefore, a wizard might cast this spell on everything in the room in order to check for mimics.

One of my favorite go-to's

If a foe is hit twice by this in the same round (both before or both after the foe's turn), either by 2 casters or via quickened spell metamagic, would the slowing effect stack? -20' instead of -10'

They would not, as it falls under the "combining magical effects" in chapter 10 of the handbook.

It would just last as long as the start of the last spellcaster.

Shoot a Water Elemental with this and it can't move.  Swim, sure.

no, it effect all movement speeds

I read it as reducing the spell's range, so it becomes 50ft next time. Though I'm new to this.

IF you hit something immune to cold damage, would they still take the -10 movement effect?

I would assume so, much like how chill touch would still impose disadvantage on a banshee's attacks. Spell rider effects that depend on the creature taking damage to apply would explicitly say so.

Can it slow down constructs?

Yes, the only condition for procing the speed reduction is making the attack roll. It would require an explicit "this creature's speed cannot be reduced" type effect to have the attack hit but not reduce the speed.

all

If your movement speed is 30ft and you are hit with this and if you dash, do you move 40ft or 50ft?

I’d assume it would be 40. “…you gain extra movement for the current turn. The increase equals your speed, after applying any modifiers.” So you’d add modifiers (-10) and add that to your speed, making it 40.

Why isn't this on the Druid spell list?

Quote from CheeseKing1985 >>

Why isn't this on the Druid spell list?

Because it's not a druid spell.