How switch a 3v load high side, from a uC powered from same 3v?
A combination of 2N7000 (or 2N3904) (as driver) with NDP6020P (as main switch) will work for you. See this answer. 

However, you don't need to invent new wheels. The device you are looking for is called "high-side" switch. There are many of them. Here is a typical device for you, SP2525A:


The switch won't power your display until the EN is "high". So before enetering the Arduino sleep mode, turn the GPIO low. A pull-down resistor might help here.