object oriented – Snake Game design

I am designing Classic Snake game using OOPS.I will have the following classes at top level :

Game
{
Board board,
Snake snake;
}

Board
{
Cell cells[];
}

Cell
{
int x,
int y,
Type type;
}

Type
{
SNAKE,
FOOD,
EMPTY
}

Snake
{
List<Cells> snakeParts;
}

I am a little confused on following point:

Can snake be part of Board class as follow?

Board
{
Cell cells[];
Snake snake;
}

Like instead of Game class having Snake object, is it better for Board class to have snake object?Because it makes sense to say that BOARD ‘has-a’ snake instead of Game ‘has-a’ snake .