Recent supernovae (SNe) observations have motivated renewed interest in SN shock breakouts from stars surrounded by thick winds. In such events the interaction with the wind powers the observed luminosity, and predictions include observable hard X-rays. Wind breakouts on timescales of a day or longer are currently the most probable for detection. Here we study the signal that follows such events. We start from the breakout of the radiation mediated shock, finding that the breakout temperature can vary significantly from one event to another (10^4 - 10^6 K) due to possible deviation from thermal equilibrium. In general, events with longer breakout pulse duration, t_bo, are softer. We follow the observed radiation through the evolution of the collisionless shock which forms after the breakout of the radiation mediated shock. We restrict the study of the collisionless shock evolution to cases where the breakout itself is in thermal equilibrium, peaking in optical/UV. In these cases the post-breakout emission contains two spectral components - soft (optical/UV) and hard (X-rays and possibly soft gamma-rays). Right after the breakout pulse X-rays are strongly suppressed, and they carry only a small fraction of the total luminosity. The hard component becomes harder and its luminosity rises quickly afterwards, gaining dominance at 10-50 t_bo. The ratio of the peak optical/UV to the peak X-ray luminosity depends mostly on the breakout time. In early breakouts (t_bo< 20 d for typical parameters) they are comparable, while in late breakouts (t_bo > 80 d for typical parameters) the X-rays becomes dominant only after the total luminosity has dropped significantly. In terms of prospects for X-ray and soft gamma-ray detections, it is best to observe 100-500 days after explosions with breakout timescales between a week and a month.