Munich accommodation in December - do you need to book well in advance?

Hi everyone,

Sorry if this has been asked elsewhere.

We are traveling through Germany this December/January and will be basing ourselves in Munich for 7-8 nights around mid December.

In this time seeing Munich, further south etc. We don't have set dates yet and it is subject to change depending on whether we like other areas and want to stay there a bit longer etc.

Do you need to book accommodation in advance round that time or can you turn up with 1-2 nights booked and then wing it?
We just want to lock ourselves in just in case things didn't go according to plan or in case the Pension/hostel isn't what we were after.

I am just not sure what winter / December is like there and if the accommodation options are still quite open without booking too far in advance

We are looking at staying in Pensions over big hotels and would like to stay in a central part of Munich rather than further out, if that makes a difference

Thanks :-)