Network slow when workstations first starting up...... need some assistance please.

I have a 7 site network, that is 6 remote sites and a central site.  These sites are all connected via point-to-point T1 links back to the central location.  Basic hub and spoke network.  Each remote site has an Active Directory domain controller and each site is on a separte subnet as well.  All of the sites are on the same domain.  I do have voice running over these T1 point-to-point links as well.  All the workstations at each site have an IP address statically assigned to them.  

The problem is that over the last month and a half, the network as been slowing down.  This slow down is worst in the morning when employees are arriving and improves as the morning and day were on.  In the middle of the night, the PC's boot up quickly and experience no extra processing or lag. This applies to all the sites we have.   I have done the following in the last couple of months:

1.  Added GPO's to the network to control and standardize settings on the PC's.
2.  Have begun pushing out software using GPO as well.  I only have two that I have pushed out, and they are CounterSpy and GFI EndPoint Security.

It appears that traffic is overwhelming the data lines to each site in the morning and the servers are expending alot of processing power as well during this time period.  This in turn as slowed everything down, from the network speed, server speed, and workstation login speeds.  What would be the best advice on diagnosing this issue?  Best advice on setting up the GPO's to be more efficient?  Best advice on troubleshooting the network traffic and server load in the morning?

Thanks for your assistance.