AddRange to a Collection

No, this seems perfectly reasonable. There is a List<T>.AddRange() method that basically does just this, but requires your collection to be a concrete List<T>.

Try casting to List in the extension method before running the loop. That way you can take advantage of the performance of List.AddRange.

public static void AddRange<T>(this ICollection<T> destination,
                               IEnumerable<T> source)
{
    List<T> list = destination as List<T>;

    if (list != null)
    {
        list.AddRange(source);
    }
    else
    {
        foreach (T item in source)
        {
            destination.Add(item);
        }
    }
}

Since .NET4.5 if you want one-liner you can use System.Collections.Generic ForEach.

source.ForEach(o => destination.Add(o));

or even shorter as

source.ForEach(destination.Add);

Performance-wise it's the same as for each loop (syntactic sugar).

Also don't try assigning it like

var x = source.ForEach(destination.Add) 

cause ForEach is void.

Edit: Copied from comments, Lippert's opinion on ForEach.

Remember that each Add will check the capacity of the collection and resize it whenever necessary (slower). With AddRange, the collection will be set the capacity and then added the items (faster). This extension method will be extremely slow, but will work.

Here is a bit more advanced/production-ready version:

    public static class CollectionExtensions
    {
        public static TCol AddRange<TCol, TItem>(this TCol destination, IEnumerable<TItem> source)
            where TCol : ICollection<TItem>
        {
            if(destination == null) throw new ArgumentNullException(nameof(destination));
            if(source == null) throw new ArgumentNullException(nameof(source));

            // don't cast to IList to prevent recursion
            if (destination is List<TItem> list)
            {
                list.AddRange(source);
                return destination;
            }

            foreach (var item in source)
            {
                destination.Add(item);
            }

            return destination;
        }
    }