Full-Bridge Mosfet Vds Waveform Problem
A snubber is designed to suppress voltage spikes. In your first photo, you don't really show any spiking, so a snubber is not what you need.
It looks like the problem is insufficient gate current.  There is a drain-gate capacitance in a MOSFET that is likely causing your problem.  When you switch &quot;on&quot; and the gate threshold is reached, the drain voltage drops from a high voltage to the source voltage at a high rate of dV/dT. If your gate drive has a high output impedance, this change of drain voltage tends to drive your gate more negative through the drain-gate capacitance.  Since the gate has just passed the threshold , it is driven back below the threshold and turns the MOSFET &quot;off,&quot; as shown in your first photo.  The drain voltage rises and the gate voltage continues to increase and then the MOSFET turns back &quot;on.&quot; The same thing happens on the falling edge, except the polarities are reversed.  In you first photo, this happens once on the rising edge and two or three times on the falling edge.
When you put a capacitance across the drain to source, the rise and fall times are slowed so that the coupling from through the drain-gate capacitance is reduced.  However, your capacitor combined with your circuit's inductance forms a &quot;tank&quot; circuit with the characteristic decaying sinusoidal waveform on every edge, shown perfectly in the second photo.
To solve your problem you can put in a gate driver with high current capability that will override the coupling effect.  Or you can try a FET with lower gate-drain capacitance (which usually means a higher &quot;on&quot; resistance).  Or you could have a layout problem - make sure your traces between the gate driver and gate are short and fat.  When done right your switching time will go down and your &quot;on-off-on&quot; issue will be solved.  A capacitor across the drain-source is not usually a good idea; it just causes higher peak currents.
When you get this fixed, your switching time will decrease and your efficiency will go up.   If you have inductance in the layout, and this causes voltage spiking, then you can consider a snubber.
Good luck!