This is the clock I made for my daughters a few months ago. A little old project but still works and can be expanded.
If you are going to download and compile the code please read all comments below.

BoM (prices are taken from Aliexpress):
- MAX7219/AX7219 LED Matrix modules - $1.3/piece (now it is cheaper than I purchased, I paid about $2.15/piece and had to solder them)
- Arduino Pro Mini with ATMEGA 168 - $1.3
- RTC module DS1307 - $0.5
- cheap 5V power supply - $0.5

Software part:
- own MAX7219 driver
- own simple DS1307 RTC functions via software I2C
- 8 fonts used (from 3x5 to 6x8 pixels)
- everything fits in 16KB flash of ATMEGA168 based Pro Mini
- temperature is taken here from internal ATMEGA sensor or external thermistor

This clock has been upgraded by some additional functions.
Extra features are shown here:
   • LED Matrix Clock extension - Bluetoot...  

The source code is available here:
https://github.com/cbm80amiga/Matrix_...

NOTE: Recently added support for rotated LED Matrices

IMPORTANT - COMMON ISSUES:
- if you don't have softI2C library installed change define "#define USEHW 1" to avoid errors during code compilation
- for other kind of MAX7219 modules you can use patched max7219.h module, just replace include file; then change "#define ROTATE 0" to 90 or 270
- I have no circuit scheme but all pins and connections are defined and described in the source code
- Arduino IDE 1.6.0 was used but the code should compile in newer IDEs too