There is currently no way to do exactly what you ask, but the following will help you streamline your updates.
It sounds like you need to add nuspec files to your solution. Something like the following three files. Note the dependencies in the second two. These refer to the same dll version as common through [$version$]. This means that when you run the following command, it updates all three because the square brackets on the dependencies require a specific version of the dependent packages.
PM> update-package common
In Hudson, you will need to execute these nuspec files using nuget pack command (see Nuget command reference) and include the resulting packages in your artifacts, AND deploy them to your local nuget server. I will leave that over to you.
The other thing you would need to do is ensure that all of your assemblies get the same version for the same build. Again, Hudson can take care of this or you could use a common AssemblyInfo file.
Common.nuspec
<?xml version="1.0"?>
<package xmlns="http://schemas.microsoft.com/packaging/2010/07/nuspec.xsd">
<metadata>
<version>$version$</version>
<authors>Charles Ouellet</authors>
<owners />
<iconUrl>http://domain/Content/images/LOGO_32x32.png</iconUrl>
<id>Common</id>
<title>Common</title>
<requireLicenseAcceptance>false</requireLicenseAcceptance>
<description>full description here</description>
</metadata>
<files>
<file src="..\Common\bin\Release\Common.dll" target="lib\net40" />
<file src="..\Common\bin\Release\Common.pdb" target="lib\net40" />
</files>
</package>
Logging.nuspec
<?xml version="1.0"?>
<package xmlns="http://schemas.microsoft.com/packaging/2010/07/nuspec.xsd">
<metadata>
<version>$version$</version>
<authors>Charles Ouellet</authors>
<owners />
<iconUrl>http://domain/Content/images/LOGO_32x32.png</iconUrl>
<id>Logging</id>
<title>Logging</title>
<requireLicenseAcceptance>false</requireLicenseAcceptance>
<description>full description here</description>
<dependencies>
<dependency id="Common" version="[$version$]" />
</dependencies>
</metadata>
<files>
<file src="..\Logging\bin\Release\Logging.dll" target="lib\net40" />
<file src="..\Logging\bin\Release\Logging.pdb" target="lib\net40" />
</files>
</package>
Logging.NLog
<?xml version="1.0"?>
<package xmlns="http://schemas.microsoft.com/packaging/2010/07/nuspec.xsd">
<metadata>
<version>$version$</version>
<authors>Charles Ouellet</authors>
<owners />
<iconUrl>http://domain/Content/images/LOGO_32x32.png</iconUrl>
<id>Logging.NLog</id>
<title>Logging.NLog</title>
<requireLicenseAcceptance>false</requireLicenseAcceptance>
<description>full description here</description>
<dependencies>
<dependency id="Logging" version="[$version$]" />
</dependencies>
</metadata>
<files>
<file src="..\Logging.NLog\bin\Release\Logging.NLog.dll" target="lib\net40" />
<file src="..\Logging.NLog\bin\Release\Logging.NLog.pdb" target="lib\net40" />
</files>
</package>