Something like this?
SELECT
trustee,
CAST( event_time AS DATE ) AS event_date,
MIN( event_time ) AS first_event,
event_type
FROM mytable
WHERE
event_type = 1
AND event_time > '2010-01-08'
GROUP BY
trustee, CAST( event_time AS DATE )
ORDER BY
event_time
The trick is to group by just the date part of the event_time, ignoring the time-of-day, as well as the trustee.
Within each group, find the first time.
This won't return a record for a date if there is no data for that trustee on that date.
Update
If you're using an earlier (pre-2008?) version of SQL Server that doesn't have a built-in DATE type then you can achieve similar using CONVERT and a suitable style argument that uses only the date part of the datetime (I can't test this at present, apologies):
SELECT
trustee,
CONVERT( VARCHAR, event_time, 110 ) AS event_date,
MIN( event_time ) AS first_event,
event_type
FROM mytable
WHERE
event_type = 1
AND event_time > '2010-01-08'
GROUP BY
trustee, CONVERT( VARCHAR, event_time, 110 )
ORDER BY
event_time