I have not read all postings in this thread, I might talk the same someone may already said about.

In matrix display, there is rows * columns. Usually if the display is not too large, only one column will be powered ON at one time, so you can see if even all LEDs will be ON (worst case) so how much power you would need at a given time.

If display is too large then it is devided into more then one segments. and each segment scans as an individual unit. The full frame is devided into seperate segment and all segment scans independently from each other. In this case you have to calculate:

total number of segment * LEDs * each LED current consumption.

For indoor display you can use low imation LEDs may be 5~20mA LED would be okay for indoor Christmas lights. But if you want it to be displayed outdoor, or at the place where so much light is present then you should use Ultra-Bright LEDs (as used in big billboards). I have a data sheet in front of me for ultra-bright blue LED. Those LEDs will need 30mA as forward current and 70mA in pulse mode. If you want to flash them fast then you should calculate on pulse based current consumption, 70mA.
You have to have huge power supply, and you can not connect LEDs in series, for a matrix display, unless you want to display multiple LEDs as a single pixel but resolution will be too less then.
If you can not afford to manage huge power supply then you can try as follows:
connect a resistor in series with 110V AC direct. I havent used it by myself, but you may try it out.
Just a rough idea came in my mind, but you have to try it out yourself. Try using 98V zener in series with LED in reverse bias. If your supply is 110V, you should have 12V at anode of zener.

Rauf