The melting point of hydrogen isn't much lower than its boiling point (6K), so the temperature isn't necessarily that much of an obstacle. However, using solid fuel requires either melting it, or burning it in place. Trying to burn solid hydrogen would likely result in the whole thing flash-boiling from the radiated heat, so that's a bit of a non-starter. And having to melt fuel out of the tank is a serious problem.
However, Wikipedia notes that there are ideas to use hydrogen slush for fuel, as that will, indeed, increase density a bit. It should also reduce boil-off as long as at least some of the tank is emptied early on; otherwise, the decreasing density of the melting slush is guaranteed to require more space or a much higher-pressure tank.