How to add a zoom session on a CDF field? Is it possible?

Unfortunately this is not possible.

I don't know which version this feature was added but It is possible now using Segmented Domain.
Here are the steps:
1. Create a new domain for your CDF (so that it won't affect the standard domain) then convert to RDD and restart the application.
2. Create the CDF you want (if you haven't already) with the newly created domain then convert to RDD and restart the application (again).
3. Go to session Segmented Domains (ttgfd4122m000) and authenticate yourself into the session if it requires.
4. Create a new Package/Domain Name for your newly created domain.
5. Insert a new record using the format according to your domain. Segment Start is default to 1 if the domain doesn't have any segmentation. Alignment and Conversion depend on your format. Now it's the part where you can now specify the zoom session and zoom return field for that particular domain, which links to your newly created CDF.
6. Save and then convert to RDD and restart the application (yeah, again).

Now you should see that the CDF now have the ability to zoom into the session you just configured and it will return the desired field.

My earlier post of almost 5 years ago was before LN extensibility was born. Nowadays it is very easy to add a zoom for CDFs by implementing the Get Zoom Session and Get Zoom Return Field hooks in a session extension.