import pandas as pd

def initialize(context):  
  context.stock = sid(19725)  
  context.price_10 = context.price_12 = 0  
def handle_data(context, data):  
  time = pd.Timestamp(get_datetime()).tz_convert('US/Eastern').time()  
  minute_high = data.current(context.stock, 'price')

  if time.hour == 10 and time.minute == 0:  
      context.price_10 = minute_high  
      log.info("The price is %s at %s" % (context.price_10, time))  
  if time.hour == 12 and time.minute == 0:  
      context.price_12 = minute_high  
      log.info("The price is %s at %s" % (context.price_12, time))  
      log.info("The difference between 10 am and 12 pm is: %s" % (context.price_12-context.price_10))  
  record(price10 = context.price_10)  
  record(price12 = context.price_12)  
  record(difference = context.price_12-context.price_10)  

That worked. Although, I have a feeling you can index more appropriately with pandas:
https://pandas.pydata.org/pandas-docs/stable/timeseries.html

Miles's idea with using the '.tz_convert' method is the way to go. Since the question was " How do I do this when it seems the get_prices() method doesn't have keys for the date/time" I'll assume this is for a notebook. Actually, the index of the result from the 'get_prices' method IS a datetime.

# set the start and stop date-time.  
# note that times are specified in UTC  
start_date = '2013-01-03'  
end_date = '2013-01-04'  
my_prices_utc = get_pricing(symbols=symbols('AAPL'),  
                        start_date=start_date,  
                        end_date=end_date,  
                        frequency='minute',  
                        fields='close_price')

my_prices_et = my_prices.tz_convert('US/Eastern')


# Because of the nuances with timezones I like to create a separate hours column  
# if one wants to check for certain hours  
my_prices_et['hour'] = my_prices_et.index.hour


# Now to get only prices between certain hours one can use the '.query' method  
my_prices_et.query('hour >= 10 & hour <= 12')

See the attached notebook (the last several cells) for this in action