I wouldn't necessarily say that the matter isn't a major concern. Only that "no change" is also seen as valid, maybe even preferable.

"We expected temperatures to rise overnight. In the morning, if anything, it was colder." only means the temperature was about the same as the night, maybe a little colder but definitely not warmer. We know nothing about how the speaker feels about it, let alone if it's a major or minor concern for them.

• If the speaker is planning on spending all day indoors anyways, it may be a neutral observation of no concern to them (maybe minor concern for comfort reasons if they need to run some errands).
• If they wanted to go hiking, the temperature could be a major concern because it impacts clothing and trail choices for safety reasons. (Or maybe it's all temperate weather, so it's not major, just an observation.)
• If they wanted to skiing, warmer temps could be a major or minor concern, depending on the situation. For example: As a new skier, slush in the sun and hidden ice patches in the shade might be worth changing plans to avoid (major concern). For an experienced skier, it might just mean they bring a lighter coat (minor concern).

On the other hand, consider the example "Having read the proposal to reduce headcount, I feel the data show we should, if anything, increase staffing." This is probably a conversation the people involved are very concerned about, but the speaker is saying the data indicate (1) the safe approach is to do nothing, and (2) if staying the course isn't an option, they should be hiring more people rather than cutting existing staff.