Here's a 66% solution (lunch is over). I couldn't get the native zip to work with PowerShell but if you have PowerShell Community Extensions installed, it should be a snap to swap out the zip call
How to create a zip archive with PowerShell?
# purloined from http://blogs.inetium.com/blogs/mhodnick/archive/2006/08/07/295.aspx
# I am not smart enough to make it work. Creates an empty .zip file for me
Function ZipIt
{
    param
    (
        [string]$path
    ,   [string]$files
    )
    if (-not $path.EndsWith('.zip')) {$path += '.zip'} 
    if (-not (test-path $path)) { 
      set-content $path ("PK" + [char]5 + [char]6 + ("$([char]0)" * 18)) 
    } 
    $zipFile = (new-object -com shell.application).NameSpace($path) 
    #$files | foreach {$zipfile.CopyHere($_.fullname)} 
    foreach($file in $files)
    {
        $zipfile.CopyHere($file)
    }
}
# this script is reponsible for enumerating subfolders
# for each file it finds, it will test the age on it
# returns an array of all the files meeting criteria
Function Walk-SubFolder
{
    param
    (
        [string]$RootFolder
    )
    $searchPattern = "*.*"
    $maxAge = 90
    $now = Get-Date
    # receiver for the files
    [string[]] $agedOutFileList = @()
    foreach($file in [System.IO.Directory]::GetFiles($RootFolder, $searchPattern, [System.IO.SearchOption]::AllDirectories))
    {
        # test whether the file meets the age criteria
        $age = [System.IO.File]::GetLastWriteTime($file)
        $days = ($now - $age).Days
        if (($now - $age).Days -ge $maxAge)
        {
            # this needs to be archived
            Write-Host("$file is aged $days days")
            $agedOutFileList = $agedOutFileList + $file
        }
    }
    return $agedOutFileList
}
Function PurgeFiles
{
    param
    (
        $fileList
    )
    foreach($file in $fileList)
    {
        # this should be in a try/catch block, etc, etc
        [System.IO.File]::Delete($file)
    }
}
$sourceFolder = "C:\tmp\so"
$zipFile = "C:\tmp\so.zip"
$oldFiles = Walk-SubFolder $sourceFolder
ZipIt $zipFile $oldFiles
#This is commented out as the zip process is not working as expected
#PurgeFiles $oldFiles
I'll see if I can work on it later to get the zip working as expected.