Using SSL private key for cookie's HMAC

[Simon Zuckerbraun <szucker () sst-pr-1 com>]

I'm pondering a design question regarding a web application that is to 
operate over SSL. We want to include an HMAC in our cookies to prevent 
tampering. To produce an HMAC, the server must be configured with a 
private key.

Since the website operates with SSL, the server already *has* a private 
key available: the private key of its SSL certificate. Is there any harm 
in using this same private key for producing the HMACs as well?

Thanks,
Simon