If you pay white mana to activate an ability that can only be activated by spending another color of mana, then any limitations on activating the ability (such as the number of times it can be activated each turn) still apply as if you spent the proper color.

The effect to turn all your non-land cards (including artifacts) white is the effect of a static ability. Thus, a color change on a permanent prior to Celestial Dawn entering the battlefield will be overridden by Celestial Dawn's effect.

You may use a different color mana than the color required for spells and abilities that require a specific color. If you do, and the spell or ability checks the actual color of the mana, it can tell the difference.

Celestial Dawn no longer changes mana symbols on cards.

Celestial Dawn does not change the type of lands which are not on the battlefield. Lands not on the battlefield are what they say they are.

Will not add or remove Snow Supertype from a land.

Mana produced by spells you control and nonland permanents you control isn't affected by Celestial Dawn. Llanowar Elves will produce , for example. However, any colored mana may be spent only on the colorless part of costs.

Land cards you own that aren't on the battlefield aren't changed to Plains.

If you have unspent nonwhite mana when Celestial Dawn enters, you still have that mana, but you can spend it only on the colorless part of costs.

If a permanent enters while Celestial Dawn is on the battlefield, and then Celestial Dawn leaves the battlefield, the permanent's color will revert to the colors in its mana cost.

If you use a text-changing effect such as Mind Bend on Celestial Dawn to change the word "Plains" to a different land type, your lands are all of that new land type, and they will produce mana of the appropriate color for that type.

If a nonbasic land has an ability that causes it to enter the battlefield tapped, it will lose that ability before it applies. The same is also true of any other abilities that modify how a land enters the battlefield or apply "as" a land enters the battlefield, such as the first ability of Cavern of Souls.