Thanks for the help .. what a great community 
So by a "cold wallet", or "cold storage" you mean a hard copy printout of the private keys?
What I am currently doing is regularly (once a month) converting some cash savings to bitcoin using ANXPRO, and sending the bitcoin to my multibit address. I keep backups of my multibit wallet. If I import my private key to Mycelium, will it be the same address as in multibit and if so what happens to the random address that Mycelium created on startup?
Can I import the multibit wallet directly into Mycelium or only the private keys?
Thanks again
Andy
If you import a private key from Multibit to Mycelium you will see the same balance and be able to spend from it in both places. This is however not a good idea:So by a "cold wallet", or "cold storage" you mean a hard copy printout of the private keys?
What I am currently doing is regularly (once a month) converting some cash savings to bitcoin using ANXPRO, and sending the bitcoin to my multibit address. I keep backups of my multibit wallet. If I import my private key to Mycelium, will it be the same address as in multibit and if so what happens to the random address that Mycelium created on startup?
Can I import the multibit wallet directly into Mycelium or only the private keys?
Thanks again
Andy
1. Instead of exposing your funds to one potentially compromised computing environment you expose it to two.
2. You may get confused as to why money went away from one wallet when spending from another.
3. You may cause double spends if you send from both wallets at or near the same time.
Instead I suggest that you have your Multibit address (not private key) imported in Mycelium, which allows you to observe, but not spend, the funds.
If you wish to spend from both wallets it is best to let them each have their own private keys.
If we are talking about savings and not 'beer money', then I would not have the funds online at all. Put them on paper and do cold storage spending:
https://www.youtube.com/watch?v=jV-29RFU6xA