Yes, the temperatures in the weeks before a hard freeze are critical in determining how well the trees will respond.
Here is an excellent article about the relationship between cold acclimation and hardiness of citrus trees using field data from FL.
http://fshs8813.wpengine.com/proceedings-o/1984-vol-97/33-36%20(YELENOSKY).pdfFigure 2 in the article is particularly useful as a guideline to determine if your citrus have accumulated a sufficient number of hours of temps below 50F but above freezing to induce full cold hardiness. For my outdoor trees here in MA (and since I provide minimal heating for them during the winter), it is critical that I know my trees are fully hardened off before allowing them to experience temps in the low 30's F or below.
Also, there is significant evidence with citrus that even cold acclimated trees will loose a significant portion of their hardiness during subsequent cold spells that occur after the first round of temps in the 20's or below. In addition to the absolute low temperatures, this is likely one of the primary reasons citrus do not grow well further north where winters last significantly longer (i.e. there is s significant probability of multiple cold snaps per winter) without a good deal of help.