If the temperature range is, say, close to freezing, or some maximum safe temperature for an activity or crop, then the error bound tells you how certain the forecast is, and whether or not an adverse condition might be experienced, for which you might want to take precautions (cover plants to protect them from freezing, ensure that they're watered for heat, say).

A minor amount of imagination can transform this question into "what should we do when the forecast says the low temperature overnight will be 2-6 degrees, but it's actually -1? If you think the forecast will tell you "whether or not an adverse condition might be experienced", you're likely to do something stupid. A more sensible approach would be "if it's frost season, cover the plants".

Weather forecasts already treat the odds differently depending on (a) what they are, and (b) what events are being predicted. A 70% chance of rain tomorrow might be reported as a 70% chance of rain, but a 10% chance of rain is more likely to be "overreported", say as a 40% chance. They do that because people don't want accurate numbers -- instead, they get mad when the forecast suggests that they don't need to prepare for unfavorable weather, and unfavorable weather inconsiderately happens anyway.

If you're a homeowner and you've got a small garden or some potted plants, covering them in straw or bringing them indoors isn't a major concern.

If you're a farmer with a crop that may need to be harvested, smudged, or sprayed with water (ice coating protects some crops), with a nontrivial investment of time and materials, the distinction is meaningful.

If you're a farmer with a crop that may need to be harvested, smudged, or sprayed with water, losing everything to frost is the kind of thing that might drive you to bankruptcy. Say there are 30 days over the course of winter where the overnight low temperature is forecast near but above zero. By your assumption, the forecast is using 95% confidence intervals. What are the odds of your crops dying if you rely on the weather forecast?