'Out in' doesn't mean anything - you are dividing the phrase up wrongly. But if you think about it as '"A tiny field mouse [had been out] [in the wood] that day gathering nuts", it makes sense. To be 'out' means to be 'outside', or away from home. 'In the wood' means exactly what you'd imagine. Here are some similar examples: 'You look suntanned.' 'Yes, I've been out in the garden all day' This means that I have been [outside the house] + [in the garden]. Or 'I love being out in the countryside in nice weather', meaning [away from the city/out of doors] + [in the countryside]. I hope that helps.

what dies it mean you look suntanned

If you mean, is the mouse still in the wood, then the answer is no. He (or she) had been out in the wood, meaning it occurred in the past and that event is now over. So the mouse has now come back from the wood and is no longer there.

In addition, Is this mouse in the wood?