Does hyaluronic acid need to be applied to damp skin to stop it pulling moisture from skin and leaving it drier?

I can see why you ask this as hyaluronic is a humectant so draws moisture to itself; it doesn't much care where that moisture is.

Having said that, it can’t drill down into your own supplies of hyaluronic acid and leach them of moisture. Pretty much anything you put on the skin is only going to make a difference to the top layer (and this is a good thing!). Some constituents can stimulate reactions in the skin that then may affect the function or systems deeper down, but mostly, you are just treating the surface.

Hyaluronic acid in significant amounts, will draw moisture to itself( this is true of most humectants: glycerine, sorbitol etc). How deeply it can penetrate is debated and depends on various factors, including the molecular size - not all hyaluronic acids are made equal(!) - the sodium hyaluronate is smaller, so theoretically can be absorbed more efficiently. However the larger HA molecules does a very good job of keeping the top hydrated - so using both together is probably a good idea.

If you are applying it in a cream or serum, it will have been manufactured with a water element in the product, so that provides the dampness, you don’t need to worry about giving it water to work with - although it won’t do any harm. It could possibly dilute the action of other active components in there, but again, the affect would be minimal.

A well made product containing HA is unlikely to make your skin feel drier and extremely unlikely to draw moisture from your own stores of HA. It should give the skin surface a smooth texture and feel well hydrated. If it has been put together intelligently with other ingredients, these can get to work under the ‘umbrella’ of the plumped up skin it provides. If it were used in a very high percentage, mixed with a very occlusive ingredient, and you were in a very dry climate, it is possible that the skin might eventually feel tight and start to look tired as the only water source is you - but that’s quite an extreme situation!

You can apply it to damp or dry skin. Warm skin might absorb it better due to the sebum becoming loosened and more liquid, so the product you apply can then get down a bit further.