RAW - No, Otto's Irresistible Dance is not a Charm spell
It does not say that the target will be "charmed", and the condition it imposes is significantly different than the description of the "Charmed" condition.
OID:
A dancing creature must use all its movement to dance without leaving its space and has disadvantage on Dexterity saving throws and attack rolls. While the target is affected by this spell, other creatures have advantage on attack rolls against it.
Charmed:
A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects. The charmer has advantage on any ability check to interact socially with the creature.
A dancing creature can attack the caster (with disadvantage -- and that disadvantage applies to any attack, not just against the caster) and can cast AoE spells that include the caster and anyone else they choose in the target area with no penalty. They just can't move freely. A charmed character can move freely but can't attack or target the caster.
Furthermore, if it were a Charm spell, it would not be necessary to specify that "[c]reatures that can't be charmed are immune to this spell." That appears to be listed as a special exception.
RAI - No, Otto's Irresistible Dance does not impose the Charmed condition
Jeremy Crawford has tweeted saying:
Being charmed means being subjected to the charmed condition
Since OID does not impose the Charmed condition, the Fey Ancestry resistance to "being charmed" does not apply.
What makes sense?
Webster's dictionary says:
charm: to affect by or as if by magic : compel
Magically forcing someone to dance seems to fall completely within that definition.
I would give those with Fey Ancestry advantage on saves against all enchantment spells that compel the user to do something that is not their own free choice. This includes many spells that do not specifically say they are "charms" or that they impose the "Charmed" condition, such as command, compelled duel, and yes, Otto's irresistible dance. I believe those all fall within the common sense and dictionary definitions of "charmed" in this context, and there's nothing in the description of Fey Ancestry that says it only applies to things that grant the "Charmed" condition.
It's pretty clear
The spell says exactly what it does.
Choose one creature that you can see within range. The target begins a comic dance in place: shuffling, tapping its feet, and capering for the duration. Creatures that can’t be charmed are immune to this spell.
A dancing creature must use all its movement to dance without leaving its space and has disadvantage on Dexterity saving throws and attack rolls. While the target is affected by this spell, other
creatures have advantage on attack rolls against it.
As an action, a dancing creature makes a Wisdom saving throw to regain control of itself. On a successful save, the spell ends.
(From SRD, emphasis mine)
- You lose all your movement (you cannot move from that place)
- Disadvantage to Dex saves and attacks
- Advantage to all attack vs you
- You may spend your action to re-do a save
That's it. It is not as ultimate as the 1-3.x version of the spell. But still hilarious. It becomes much more of a combo spell than before, especially if you can throw Dex-save spells on the enemy or can move away from it.
As an action, the spell is clear that all you do is make a new save.
Best Answer
You can make your save before losing your move...
From the text of the spell (PHB 264, emphasis mine):
Note the term "use" rather than something like "lose" or "have its speed reduced to 0". The spell compels you to move your speed within a 5 foot square. Fortunately, from the description of a player's turn (PHB 189):
Even better, if slightly contradictory (PHB 190):
In this edition, players are given a great deal of latitude on when to use their movement. Since dancing is a use of that movement, you can choose to save before using it up.
It helps to think about what limits your movement speed under regular circumstances. Remember that a round, and thus a turn, lasts ~ 6 seconds. When your move speed is 30 feet, it doesn't mean you are out of breath after running 30 feet, it means that it takes you about 6 seconds to move that distance with enough time left over to do something else. Dancing keeps you from moving anywhere as the clock ticks down, but if you make your save quickly, nothing in the wording of the spell suggests you would be prevented from using the remaining time in your turn to move your speed.
...but you still dance
You start dancing as soon as the spell is cast, with all of the attendant detriments (disadvantage on attacks and Dexterity saves, granting advantage to attackers). There isn't much you can do about that until the start of your turn, but at least you don't have to stay immobilized.