>>>Who decides if a flight is cancelled, the company or pilots?
Let me preface my answer by noting that my answers are based upon US FAR Part 121 Domestic/Flag rules... Other Reg scenarios by other airlines in other countries might parallel US FARs, but may also vary greatly....
Under a US Part 121 Domestic/Flag scenario (including flights dispatched from the US to other international destinations) the PIC and dispatcher are jointly responsible for the safe conduct of the flight, including the operational control of the flight. If the weather forecasted for the destination airport required it, an alternate airport (and the fuel to reach it) would be called for, as well as fuel for holding, deviating around storms, along with other fuel for the appropriate contingencies, as well as reserve fuel.
Maximum wind limits vary among aircraft models, but generally speaking, many aircraft have a 30-knot crosswind limit on a dry runway. If the runway is wet, or the visibility is below 3/4 mile or RVR 4000, the max crosswind limit drops to 10 knots. If the runway has degraded braking action from snow, slush, water, etc., the crosswind limits could be down to 5-knots. All these limits are spelled out in the airline operator's manuals and Operations Specifications (Ops Specs), and compliance with them is required by FARs.
Should a crew be unable to land due to some parameter being out of limits (vis, wind, etc.) they will contact their dispatcher via radio (either voice, or text via ACARs) and advise them of their situation and fuel onboard. Some weather can be variable, i.e. thunderstorms move, foggy visibility may fluctuate up/down from one moment to the next, etc., so the PIC and dispatcher work out a mutually acceptable plan to hold down to X-amount of fuel and them proceed to their alternate. That alternate has to meet its own weather criteria, and may also consider where the particular airline has its own personnel and facilities (online) or somewhere else it doesn't (offline) but that may have better weather. Lots of other variables too.
If the weather situation shows no signs of improvement, flights can be, and are cancelled, and that's accomplished by the airline's dispatch office, usually management personnel. Should they say "go" when it's not safe to do so, the dispatcher and PIC have legal obligations not to operate, and they don't, since the dispatcher and PIC are the only two individuals who have signed the flight's dispatch release, and are subject to license action on FAR violations.
ALL views, opinions expressed are mine ONLY and are NOT representative of those shared by Southwest Airlines Co.