As AA Milne died in January 1956 his works will be protected by copyright until 1st January 2027, that is to say, for 70 years from the end of the year of his death.
However, provided that the extract you would like to use is fairly short, you can take advantage of an exception to the general copyright protection for the purpose of quotation, without the need to get formal permission. The legal authority for this is Section 30
(subsection 1ZA) of the Copyright Designs and Patents Act 1988. But note that you must include a credit for the quotation, so for instance you might put the author's name and the title of the actual Pooh book beneath the quotation.
In theory there is nothing to stop you using the same exception to include an illustration from the original book as well, although since the artist for these was EH Shepard, you should also provide a separate credit to him if you did want to do this. These exceptions come under the heading of 'fair dealing', which means you should not use more of the original than is essential for your purpose. I imagine you might want to include something about the Hundred Acre Wood, or a description of how to play Pooh-sticks, if that forms part of your picnic plans.
If you feel it is necessary to quote more than an average person might regard as 'fair', then there is nothing to stop you para-phrasing parts of the stories in your own words, and incorporating brief snippets of Milne's actual text to add authenticity to project. Just make sure that if you do this, you still include the necessary credit somewhere on the display board.
I would advise you to stick the original Milne stories and Shepard illustrations rather than using anything from the modern TV or Film adaptations of the stories, since the production companies (like the Disney Corporation) involved in these spinoffs are far more likely to object than Milne's estate might.
And a final word of warning about the use of the words "Winnie the Pooh". Disney have registered
these words as a trade mark for, amongst other things, 'education; providing of training; entertainment; sporting and cultural activities'. Since this could arguably stretch to include your picnic activity, I suggest that you don't make the words a major part of your advertising for the event. It is worth stressing that as you are not charging for the event your use would not infringe these trade marks because your use would not be in the course of trade. Nevertheless, Disney employ third party companies to continually trawl the internet for possible infringements using automated processes, and this could result in you receiving unwelcome, albeit unjustified, attention from their lawyers even though you would not be doing anything wrong.