Wine allows you to run windows apps on a Linux PC via a virtual machine.
I used wine with Linux for a while and it came in handy sometimes. Today I found the need to launch a windows app but couldn't and it just made me think about wine.
Update for those who want to know. As of now the answer for wine is no.
Long story short...
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Thunderbird: No, it is not possible. The main issue (next that you need a x86 cpu which likely your netbook has) is that Android is not a typical Linux system. The OS uses the Linux kernel but apart from that it uses very different libraries, it doesn't use X and so on.