Could you please advise me on the risks involved in deploying distributed firewalls?
A traditional firewall is used to separate an internal network from the Internet. This provides some level of protection against attacks that come from external sources, but does nothing to prevent insider attacks.
Distributed firewalls are typically software products that reside on each individual computer on the network, so that protection is provided against attacks coming from anywhere.
If one is going to use distributed firewalls (and they're not a bad idea), don't give up your traditional firewall. The sooner an attack can be stopped, the better off you are. Your traditional firewall can hide the details of your internal network and prevent your internal machines from even being attacked by external sources.
The biggest problems with the distributed firewalls are the following:
 Consistent application of firewall rules.
 Interference with standard applications.
 Users blaming problems on on the firewall software.
It is very possible that the firewall software will cause problems with standard applications. Your users will not be at all happy with that. Even if the firewall software does not cause problems, it will be blamed for problems that do occur, and the security support staff will have additional help-desk work. Keeping every machine up to date with the latest firewall rules will be a logistical nightmare. However, some products are coming out with centralized management tools to help with those problems.
So, the short answer to your question, is that the security risks of using distributed firewalls are minimal, as long as you also keep your traditional firewall. If you give up the traditional firewall, you are exposing each of your networked computers to individual attack, instead of hiding them behind the firewall. That is a risk that I would not recommend.