Why can't C# SMO see extended properties on a column but Powershell SMO can?
I just want to shadow @BradC a little.
I tested his code on Visual Studio 2015 (Update 3) on a Windows 10 Pro x64 machine against an SQL Server 2014 instance and I can confirm you can get Extended Properties of a field without issues.

To replicate I use one of my local databases. I used the following code snip to define some extended properties.

USE MyLocalDb;
GO
EXEC sys.sp_addextendedproperty 
@name = N'MS_DescriptionExample', 
@value = N'Some EP example.', 
@level0type = N'SCHEMA', @level0name = dbo, 
@level1type = N'TABLE',  @level1name = tblATableWithAtblPrefix,
@level2type = N'COLUMN', @level2name = Forename;
GO


I created a new console project and added the following references:

Microsoft.SqlServer.ConnectionInfo
Microsoft.SqlServer.Management.Sdk.Sfc
Microsoft.SqlServer.Smo
Microsoft.SqlServer.SqlEnum


All from:


  \%Install Path%\Microsoft SQL Server\130\SDK\Assemblies\


So my whole code, based on @BradC's looks like:

using System;
using System.Data.SqlClient;
using Microsoft.SqlServer.Management.Smo;
using Microsoft.SqlServer.Management.Common;

namespace ConsoleApplication7
{
    class Program
    {
        private static Database database;
        static void Main(string[] args)
        {
            Microsoft.SqlServer.Management.Smo.Server server;

            SqlConnection connection = new SqlConnection("Integrated Security=SSPI; Data Source=SIS_DBA");
            Microsoft.SqlServer.Management.Common.ServerConnection serverConnection = 
                new Microsoft.SqlServer.Management.Common.ServerConnection(connection);

            server = new Server(serverConnection);

            database = server.Databases["ImmigSql"];

            foreach (Table table in database.Tables)
            {
                Console.WriteLine(" " + table.Name);
                foreach (Column col in table.Columns)
                {
                    Console.WriteLine("  " + col.Name + " " + col.DataType.Name);
                    foreach (var property in col.ExtendedProperties)
                    {
                        Console.WriteLine(" " + property.ToString() + "");
                    }
                }
            }
            Console.ReadLine();
        }
    }
}




Of course you can now access the properties and use their values.

The Count value that wasn't working on your example: