Hi Brian,
I would import the horizon AS IS and change the values in OpendTect. If you are a Pro user you can use Horizon Mathematics to replace all values close to zero to real zeros or undefined values (undef or 1e30). The formula looks like this:
(Zval < C0 && Zval > -C0)? 0 : Zval
Where Zval is the Z value of the input horizon and C0 is a constant.
If you use the community version, you can do the same in the attribute engine using the Mathematics attribute. Apply the formula to the horizon and save as horizon data. Export the horizon data and re-import as a new horizon.
Best regards,
Paul.