private void ColorBtn_Click(object sender, EventArgs e)
{
    var btn = sender as Button;
    var color = btn?.Name == "RedBtn" ? Color.Red : Color.Green;

    Controls.OfType<CheckBox>()
        .Where(x=>x.Checked)
        .ToList()
        .ForEach(x=>x.ForeColor = color);
}

public partial class Form1 : Form
{
    public Form1()
    {
        InitializeComponent();

        ReadColorCheckBoxes();
    }

    private void buttonGreen_Click(object sender, EventArgs e)
    {
        SetBackColorCheckBoxes(Color.Green);
        SaveColorCheckBoxes();
    }

    private void buttonRed_Click(object sender, EventArgs e)
    {
        SetBackColorCheckBoxes(Color.Red);
        SaveColorCheckBoxes();
    }

    private void SetBackColorCheckBoxes(Color color)
    {
        var checkboxes = GetCheckedCheckBoxes();

        foreach (var checkbox in checkboxes)
        {
            checkbox.BackColor = color;
        }
    }

    private void SaveColorCheckBoxes()
    {
        var checkboxes = GetCheckedCheckBoxes();

        foreach (var checkbox in checkboxes)
        {
            Properties.Settings.Default[checkbox.Name] = checkbox.BackColor;
        }

        Properties.Settings.Default.Save();
    }

    private void ReadColorCheckBoxes()
    {
        foreach (var checkbox in this.Controls.OfType<CheckBox>())
        {
            checkbox.BackColor = (Color)Properties.Settings.Default[checkbox.Name];
        }
    }

    private IEnumerable<CheckBox> GetCheckedCheckBoxes()
    {
        return this.Controls
                            .OfType<CheckBox>()
                            .Where(c => c.Checked == true);
    }
}