Connect 4 C# checking wins problem

You didn't tell us in which way your method CheckHorizontal(..) does not work and I find it not very intuitive to read, so I'll just show you how I would do it:

Declare an array of X/Y-tuples which describe the translation from the position at which the method currently "looks at" to the next position, for 0°, 45°, 90° and 135°. For the tuples I'd use a custom class to avoid the "Item1", "Item2" property-names of the inbuilt Tuple<,> class. I'm setting the origin of the coordinate system in the lower left corner.

// pseudocode:              N        NE       E      SE
array directionSteps = { {0, -1}, {1, -1}, {1, 0}, {1, 1} }

The remainder explained in comments:

// semi-pseudocode:  

int xCenter = ...   // x-coordinate of tile placed last
int yCenter = ...   // y-coordinate of tile placed last
int tileColor = ... // value of tile placed last (probably 1, resp. 2)

// outer loop loops over those direction-steps N, NE, E, SE:
foreach (directionStep in directionSteps)
{
    int matchingTiles = 1; // tile placed last is the first match

    // to check each direction also into the opposite direction
    // have a multiplier of -1 / 1 for each of them:
    for (int directionUpDown = -1; directionUpDown <= 1; directionUpDown += 2)
    {
        int xStep = directionStep.X * directionUpDown;
        int yStep = directionStep.Y * directionUpDown;

        // "walk" into the current direction, starting 1 tile away;
        // distance will be 5 at maximum
        for (int distance = 1; distance <= 5; distance++)
        {
            // now "looking" at these coordinates:
            int x = xCenter + xStep * distance;
            int y = yCenter + yStep * distance;

            if (IsOutsideOfGrid(x, y))
                break;

            if (Grid[x, y] == tileColor)
                matchingTiles++;
            else
                break;
        }
    }

    if (matchingTiles >= 4)
        // player with that tileColor has won
}