Script to view all printers and set default printer remotly

good Afternoon 

I have the below scrip the first piece works great im able to view which printers are connected to the machine, granted it wont tell me which one is set to default.

But i can't seem to have the second part of the script to work which is to ask me which printer i would like to set up as default and then set it. I know its not working since im not sure what is the best way to connect to the remote PC and run the command but it does work if i run the second part of the script on the local PC which defeats the purpose. Any help will be greatly appreciated

Thank you   

$x = read-host -prompt "Please enter the machine name:"
Get-WMIObject Win32_Printer -ComputerName $x

Write-host "Would you like to change the default printer ? (Default is No)" -ForegroundColor Black
$Readhost = Read-Host " ( y / n ) "
Switch ($ReadHost)
{
Y {$printerdef=Read-Host -Prompt "what printer would you like to set as default"
(New-Object -ComObject WScript.Network).SetDefaultPrinter($printerdef)}
N {Write-Host "Default printer will not change"; $PublishSettings=$false}
Default {Write-Host "Default, No change"; $PublishSettings=$false}
}