You should update to the latest version of Snow Leopard, 10.6.8 - you can download it here; however it's still not compatible with iCloud and though you can connect to access your email you cannot access any other of iCloud's facilities.
However some people have been able to set up calendar syncing by using the method detailed here - this is an unsupported hack and may not be reliable, and may stop working at some future point. I've not tried it: use at your own discretion.
To access the email:
Are you sure you can't upgrade to Lion? It requires an Intel Core 2 Duo processor, which you may well have, though it also needs 2GB RAM so you might need to add additional RAM (might not be worth it for what you want). The published specs don't mention 32 or 64 bit. You can buy Lion by ringing the Apple Store at the number at bottom left of this page.
This worked perfectly. Thank you, and the comments for getting pxx values made that easier than expected.
I did originally try to get to 10.8.2, but the MacBook wouldn't run the disk I have. A little further research about 10.8 suggested that my MacBook is too old. And my search for a solution led me to a Support discussion that concluded that the switch to 64 bit is the problem.
There might be a workaround, but I'd suspect it's above my abilities, even with help. And this solution does what I need.