Card Game - Assign Cards to Player

So I have made a simple Windows Form that creates a deck of cards and has a button that shuffles cards and displays them in to 52 text boxes.  I am trying to figure out how to assign these cards to a certain player, such as text box 1-13 would be player 1, and then to compare the cards and put them in numerical order.  I don't really know how to start doing this as this is my first card game. 

In addition to the code I have below, I have:

TextBox[] boxes;

Random r = new Random();

string[] cards (contains all possible values i.e. "A♠" or "3♣")

Here is my current buttonClick:

        private void button1_Click(object sender, EventArgs e)
        {
            int cardCount = cards.Length;
            int[] cardIndexList = new int[cardCount];

            for (int i = 0; i < cardCount; i++) { cardIndexList[i] = i; }

            foreach (TextBox box in boxes)
            {
                int cardIndex = r.Next(cardCount);
                string card = cards[cardIndexList[cardIndex]];
                cardCount--;
                cardIndexList[cardIndex] = cardIndexList[cardCount];
                box.Text = card;
                box.ForeColor = (card.Contains("♥") || card.Contains("♦")) ? Color.Red : Color.Black;
            }
        }

Also, eventually I will be changing the text boxes to picture boxes. Is there a good time to do that, such as now?  How much difficulty is involved in that?