1. On the Admin menu, select System > Configuration. Then in the panel on the left, under General, click Web.
2. Expand the Session Cookie Management section
3. Set the Cookie Domain to .example.com (be aware to put that first dot in).

1. On the Admin menu, select System > Configuration. Then in the panel on the left, under General, click Web.
2. Expand the Session Cookie Management section

In the example.com shop, set the following:

3. Set the Cookie Domain to example.com (usually this setting would be .example.com with a dot in front, you might try it without in this case).

In the test.example.com shop, set the following:

4. Set the Cookie domain to .test.example.com on the test-environment. (the "." in front of the domain should be fine here)