Lack of Explicit info
The answer is: We do not know.
There is no mention in the books about the training procedure for the ravens whether they be black or white.
So the following would be just speculation based on logic and canon evidence.
Attaching a note to the bird
Maesters can attach notes to the white birds to notify the recipients that it is a drill and not a herald of Winter's arrival.
In Westeros, Seasons are more fickle than sellswords or Ironborn. For instance, see the year of false Spring when everyone thought that Winter was over when in fact it wasn't. So odd timing of arrival of a white raven alone won't lead to the conclusion that this may have been just a drill.
Which means that the maesters would have to explicitly communicate to the lord concerned that his castle may host a trainee bird. This can be done by:
- Attaching a note to the White bird with explanation.
- Notifying the lord via a black raven prior to the flight of the white raven so that the hosts are prepared to see the winter bird.
Meetings of Lords
When winter is actually on the horizon, regional lords hold a summit with their overlords to decide what portion of the harvest is to be set aside as reserve for winter.
For example, in ACOK, we see Northern Lords or their representatives arriving in Winterfell for a Harvest feast where they asked the Starks about food provisions for the upcoming winter.
From ACOK, Bran II:
Bran soon realized that it was the steward, not Lady Glover, who truly
ruled at Deepwood Motte. The man allowed that he was at present
setting aside only a tenth of his harvest. A hedge wizard had told
him there would be a bountiful spirit summer before the cold set in,
he claimed. Maester Luwin had a number of choice things to say about
hedge wizards. Ser Rodrik commanded the man to set aside a fifth
From the same chapter:
When the morrow came, most of the morning was given over to talk of
grains and greens and salting meat. Once the maesters in their Citadel
had proclaimed the first of autumn, wise men put away a portion of
each harvest... though how large a portion was a matter that seemed to
require much talk. Lady Hornwood was storing a fifth of her harvest.
At Maester Luwin’s suggestion, she vowed to increase that to a
So let's say even if a Lord was mistaken in actually believing that Winter was indeed coming for any reason, he would then send a delegation or a message to his overlord about the portion of harvest to be stored which would then confirm that Winter isn't actually coming.
Local Maesters themselves appear to keep record of seasons in addition to the records kept by the central Citadel in Old Town. For example, Maester Aemon kept his own readings of seasons and did not solely rely on readings of the citadel.
From AGOT, Tyrion III:
The Lord Commander did not seem amused. “You are not fool enough to
believe that, my lord. Already the days grow shorter. There can be no
mistake, Aemon has had letters from the Citadel, findings in accord
with his own. The end of summer stares us in the face.”
So in event of receiving such a bird, local Maester might be able to figure out that it is just a drill even if there was no notification of that.