I saw a ruling on this before, but I can't find it now. If you begin in clear terrain, have the foot symbol, and charge so that your last square of movement ends in hindering terrain, can you complete your charge and attack?

Yes. The hindering terrain causes your movement to end. And the attack in Charge comes at the end of the movement.

So long as the last square you end in hindering puts you adjacent to your target yeah. And if you're worried about Hindering stopping you, slap Unstoppable and for extra fun Movethrough and you can charge whoever you want so long as you've got the distance and a clear space next to your target to end at.

Fixed it for you

Since you can't use the free attack against terrain when Charging (that part of Unstoppable only works with move actions and Charge is a power action), 9 times out of 10 I'll use Swingline instead. As long as the Charge character has the boot movement symbol, not only does it get to ignore hindering terrain when moving, but it also gets a +1 bonus to movement (which usually rounds up to an extra square of Charge!!!). True, it does cost 10 points instead of 5, but I think the difference is worth it.