Do I need an antivirus program in each virtual machine?

No, you should not be using AV software on the host to scan your VHD location. You can install AV software on the host but you need to exclude several Hyper-V related folders from the real time AV scanning engine and from any scheduled AV scans. You should then install AV software on the individual guest virtual machines.

https://support.microsoft.com/en-us/kb/961804

You need to install AV which is specially designed for Hyper-V. It will install itself into host but it will scan VMs and their vRAM, on-disk images and also intercept traffic between VMs and host routed over vSwitch. 5nine has one (I'm not working for them it's just an example).

http://www.5nine.com/5nine-security-for-hyper-v-product.aspx

@BaronSamedi is right, best approach is a VM-aware agentless AV solution. 5nine has 3 AV options to choose from including Vipre, Kaspersky, and IIRC ThreatTrack. An alternative may be ESET, they recently started offering agentless specifically for virtualized environments.