It's already cold all day. My gladioli feel bad: buds open poorly, droop. Is it possible to transplant them into the greenhouse? If, say, take and dig deeper, along with a lot of land. Their roots are not very large. Will they take root or not?
Nevertheless, they gave you the wrong advice - it is suitable for the period of vegetative growth, and not when the buds have formed. If not for distillation, then replanting in a greenhouse can hardly be considered advisable for the following reasons.
In general, gladiolus is known to belong to late-flowering plants, although there are early varieties. That is, it is still desirable to know well about the features of your climate in order to select a variety group and specific varieties, first according to the passport, so to speak, characteristics, and therefore already in practice for several seasons.
If you have late spring and early frosts in the fall, then at the beginning of the growing season, in my opinion, it is better and easier to use arcs and covering material (lutrasil / spandobod). Similarly in the fall, if you see that they do not have time to bloom to frost.
By the way, although gladioli are not like lilies, but with well-formed buds, they will also bloom at home after cutting.