What to record
Date and site, the conditions (rain, wind, snow, frost, heat), when work stopped and restarted, which activities were affected, who was standing, and any plant or labour cost. Photos and a note in the site diary help.
Why it matters
Weather is usually a delay you carry the risk for unless the contract says otherwise. Where it does give relief, you have to show the weather was unusual and that it actually delayed the work - and records made at the time are far stronger than reconstructions.
The usual contract tests
Under JCT contracts, exceptionally adverse weather is normally a ground for an extension of time but not for extra money. Under NEC4, weather is a compensation event only if the measured conditions at the place named in the contract occur less often than once in ten years. Read your own contract - amendments are common.
Back it up with data
Pair your log with recorded weather data for the area, so you can show the conditions were out of the ordinary.