Two lights are wired to one switch and we're installing one new light. The old light worked fine and now the white wire is hot. Help!

If the original wiring was a switch loop, the white is hot, but possibly not marked as such. If there are only 2 wires in the switch box, and white is connected to one of the switch terminals, it is a switch loop and would be hot. Incoming neutral goes to light white, black power feed goes to switch and white goes back to light black. Put black tape on white or use blacl magic marker.

Time out, please.

The NEC only allows the retasked Neutral (White or gray) to carry voltage away from the supply to the switch.

The Black must be used as the return to the fixture.

And yes, the retasked white conductor must be marked with a color other than gray or white at any point where it is visible.

Don is correct in his description, but sometimes folks do it wrong also.

This is the problem:
Two lights are wired to one switch and we're installing one new light. The old light worked fine and now the white wire is hot. Help!
I for one have NO idea what you are saying. All you did was change the light? That would NOT make a white wire hot. If the old fixture worked fine then you did something wrong with the new one. Unfortunately it is really hard to say what given the limited information at hand.

You are going to have to describe every wire in each box involved to give us a clue as to what is going on here.

Donf. Please cite the code reference, I haven't found it yet.

2008 NEC

200.7 Use of Insulation of a White or Gray Color or with Three Continuous White Stripes.

(C) Circuits of 50 Volts or More. The use of insulation that is white or gray or that has three continuous white stripes for other than a grounded conductor for circuits of 50 volts or more shall be permitted only as in (1) through (3).

(1) If part of a cable assembly and where the insulation is permanently reidentified to indicate its use as an ungrounded conductor, by painting or other effective means at its termination, and at each location where the conductor is visible and accessible. Identification shall encircle the insulation and shall be a color other than white, gray, or green.

(2) Where a cable assembly contains an insulated conductor for single-pole, 3-way or 4-way switch loops and the conductor with white or gray insulation or a marking of three continuous white stripes is used for the supply to the switch but not as a return conductor from the switch to the switched outlet. In these applications, the conductor with white or gray insulation or with three continuous white stripes shall be permanently reidentified to indicate its use by painting or other effective means at its terminations and at each location where the conductor is visible and accessible.

Thanks for the info. Does seem strange when both wires are used as black. What is the logic?

It's called a switch loop.There are many times when this is an easier or more economical way to wire a circuit.

Also, both wires are not being used as a black. The white is simply being used as a hot conductor, or more accurately, an "ungrounded conductor".
You can color it pink, purple, orange; just not white, green or gray.