If you want to make the code in your own answer easier to understand you can remove the duplicate code to make the if statement cleaner.

Assigning the results to variables and using those instead:

$UserName = Get-WmiObject –ComputerName $poste –Class Win32_ComputerSystem | select -ExpandProperty UserName
$WindowsVersion = Get-WmiObject -Computer $poste -Class Win32_OperatingSystem | select -ExpandProperty Version
$LogonuiProcess = Get-Process -name logonui -ComputerName $poste -ErrorAction SilentlyContinue

Then either:

if (($UserName -and $WindowsVersion -like "*10*") -or ($UserName -and -not $LogonuiProcess)) {Write-Output "do X"}

Or

if ($UserName -and $WindowsVersion -like "*10*") {Write-Output "do X"}
elseif ($UserName -and -not $LogonuiProcess) {Write-Output "do Y"}

There are various ways to go about this; but this one is clean and easy to understand, so would be my preferred route:

Function Move-FolderConditional { # todo: give this cmdlet a better name for your context
    [CmdletBinding()]
    Param (
        [Parameter(Mandatory, ValueFromPipeline)]
        [System.IO.DirectoryInfo[]]$Path
        ,
        [Parameter(Mandatory)]
        [System.IO.DirectoryInfo]$Destination
        ,
        # files matching this pattern get moved to the target
        [Parameter(Mandatory)]
        [string]$ArchivableFolderPattern
        ,
        # Files older than this date get moved to the target
        [Parameter()]
        [string]$MinKeepDateUtc = (Get-Date).AddDays(-3).ToUniversalTime()
    )
    Process {
        foreach ($directory in $Path) {
            if ($directory.BaseName -notmatch $ArchivableFolderPattern) {
                Write-Warning "Could not move folder 'directory.FullName)' as the name does not match the required pattern"
                continue;
            }
            if ($directory.LastWriteTimeUtc -ge $MinKeepDateUtc) {
                Write-Warning "Could not archive folder 'directory.FullName)' as it was last updated at 'directory.LastWriteTimeUtc.ToString('u'))'"
                continue;
            }
            try {
                #Move-Item -Path $directory -Destination $Destination -ErrorAction Stop # Uncommend this if you actually want to move your files
                Write-Information "Successfully moved 'directory.FullName)' to 'Destination.FullName)'" 
            } catch [System.Management.Automation.ItemNotFoundException] { # For this exception we'd probably check in the Begin block instead - but this is just to give the idea that we could add a try/catch if required
                Write-Warning "Could not archive folder 'directory.FullName)' the target directory does not exist: 'Destination.FullName)'"
            }  
        }
    }
}

# Example usage
Get-ChildItem $path -Directory -Force | Move-FolderConditional -ArchivableFolderPattern '^log' -InformationAction Continue -Destination 'z:\archive\'

But other options are available (I've just included snippets to give the gist of these):

Switch Statement

switch ( $directory )
{
    {$_.BaseName -notmatch $ArchivableFolderPattern}
    {
        Write-Warning "Could not move folder '_.FullName)' as the name does not match the required pattern"
        break
    }
    {$_.LastWriteTimeUtc -ge $MinKeepDateUtc}
    {
        Write-Warning "Could not archive folder '_.FullName)' as it was last updated at '_.LastWriteTimeUtc.ToString('u'))'"
        break
    }
    default 
    {
        Write-Information "Successfully moved '_.FullName)' to 'Destination.FullName)'" 
    }
}

Flags

[bool]$archiveFolder = $true
if ($directory.BaseName -notmatch $ArchivableFolderPattern) {
    Write-Warning "Could not move folder 'directory.FullName)' as the name does not match the required pattern"
    $archiveFolder = $false
}
if ($directory.LastWriteTimeUtc -ge $MinKeepDateUtc) { 
    # note: this will process even if archivefolder is already false... you can use `else` or amend the condition to include `$archiveFolder -or ($directory.LastWriteTimeUtc -ge $MinKeepDateUtc)`; though if going that route it's better to use the switch statement.
    Write-Warning "Could not archive folder 'directory.FullName)' as it was last updated at '_.LastWriteTimeUtc.ToString('u'))'"
    $archiveFolder = $false
}
if ($archiveFolder) {
    Write-Information "Successfully moved 'directory.FullName)' to 'Destination.FullName)'" 
}

Other

Or you can do combinations of the above (e.g. use the switch statement to set your flags (in which case you can optionally remove the break so that all issues are displayed).

In addition to the answer from mklement0 and avoiding the rather slow Compare-Object cmdlet:

In what you tried, you will need to compare one specific value with each of the rest of the vales:

($a -eq $b) -and ($a -eq $c) -and ($a -eq $d)

Because the Comparison Operators (-eq) take a higher precedence than the Logical Operators (-and), you can leave the brackets and simplify it to:

$a -eq $b -and $a -eq $c -and $a -eq $d

To make this code DRY and easily expandable for even more values:

if ($a, $b, $c | Where {$_ -ne $d}) {
  'different'
} else {
  'same'
}